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A064548
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Numbers n for which the sum of the binary digits (or count of 1-bits) equals the sum of the prime exponents of n+1 (or the factor-count of n+1).
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3
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1, 2, 3, 4, 5, 7, 9, 11, 15, 16, 19, 20, 23, 24, 26, 31, 33, 34, 39, 41, 44, 47, 48, 49, 53, 63, 67, 68, 69, 74, 79, 83, 89, 95, 97, 98, 99, 104, 107, 127, 132, 135, 137, 139, 144, 146, 149, 152, 159, 160, 164, 167, 179, 191, 194, 195, 197, 199, 209, 215, 242, 255
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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This sequence becomes rare for large n: 15 values between 100000 and 101024 and none between 1000000 and 1001024.
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LINKS
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FORMULA
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EXAMPLE
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8 is absent since 8 in binary is (1000) with sum=1, while (8+1) has 2 factors.
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MATHEMATICA
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Select[ Range[ 1024 ], DigitCount[ #, 2, 1 ]===(Plus@@(Last/@FactorInteger[ #+1 ]))& ]
Select[Range[300], DigitCount[#, 2, 1]==PrimeOmega[#+1]&] (* Harvey P. Dale, Mar 11 2023 *)
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PROG
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(PARI) SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } baseE(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, s=SumD(baseE(m, 2)); f=factor(m + 1)~; e=0; for (i=1, length(f), e+=f[2, i]; if (e>s, break)); if (s==e, write("b064548.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 18 2009
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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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