Search: a364960 -id:a364960
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0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 3, 0, 5, 4, 3, 0, 2, 3, 5, 0, 3, 4, 7, 0, 0, 6, 2, 5, 9, 4, 10, 0, 2, 3, 3, 4, 9, 6, 4, 0, 11, 4, 12, 5, 0, 8, 13, 0, 0, 1, 7, 7, 15, 3, 5, 6, 8, 10, 16, 5, 17, 11, 5, 0, 3, 3, 14, 4, 6, 4, 16, 5, 18, 10, 4, 7, 4, 5, 19, 0, 4, 12, 21, 5, 6, 13, 9, 6, 22, 1, 5, 9, 10, 14, 7, 0, 24, 1, 6
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OFFSET
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1,7
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LINKS
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PROG
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(PARI)
Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 341887, 393216, 524288, 683774, 786432, 1048576, 1572864, 2097152, 2495625, 3145728, 4194304, 4991250, 6291456
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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For n = 341887, A156552(n) = 1736, "11011001000" in binary, and A163511(n) = 1830711541, with A156552(A163511(n)) = 444544, "1101100100010000000" in binary, and as the former binary expansion is a prefix of the latter, 341887 is included in this sequence. In this case, 1830711541 = A003961^7(2*341887), where A003961^7 indicates a prime shift by seven steps towards larger primes.
For n = 683774 = 2*341887, A156552(n) = 3473 = "110110010001", and A163511(n) = 3661423082 = 2*1830711541, with A156552(A163511(n)) = 889089, "11011001000100000001", and as the former binary expansion is a prefix of the latter, 683774 is included in this sequence.
For n = 1367548 = 4*341887, A156552(n) = 6947, "1101100100011" in binary, and A163511(n) = 7322846164 = 2*3661423082 with A156552(A163511(n)) = 1778179, "110110010001000000011" in binary, as the former binary expansion is NOT a prefix of the latter, 1367548 is NOT included in this sequence.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A364961
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Odd numbers k such that A005940(k) is either k itself or its descendant in Doudna-tree, A005940.
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+10
3
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1, 3, 5, 25, 45, 49, 40131, 50575, 79625, 1486485, 1872507, 3403125
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OFFSET
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1,2
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COMMENTS
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Note that 1, 25, 45, 49 are so far the only known integers x for which A005940(x) = A003961(x).
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LINKS
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EXAMPLE
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Term (and its factorization) A005940(term) (and its factorization)
1 -> 1
3 -> 3
5 -> 5
25 = 5^2 -> 49 = 7^2
45 = 3^2 * 5 -> 175 = 5^2 * 7
49 = 7^2 -> 121 = 11^2
40131 = 3^2 * 7^3 * 13 -> 100847877 = 3 * 13^2 * 19^3 * 29
50575 = 5^2 * 7 * 17^2 -> 22467159 = 3^3 * 11^2 * 13 * 23^2
79625 = 5^3 * 7^2 * 13 -> 787365187 = 7 * 19^3 * 23^2 * 31
1486485 = 3^3 * 5 * 7 * 11^2 * 13 -> 25468143451205
= 5 * 7 * 13 * 17^3 * 19 * 23 * 29^2 * 31
1872507 = 3 * 7 * 13 * 19^3 -> 240245795625
= 3 * 5^4 * 11 * 17 * 23 * 31^3,
3403125 = 3^2 * 5^5 * 11^2 -> 2394659631669305
= 5 * 7^3 * 11 * 13^2 * 17^5 * 23^2.
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PROG
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(PARI)
Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
isA364961(n) = if(!(n%2), 0, my(k=A005940(n)); while(k>n, k = A252463(k)); (k==n));
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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