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A282774
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Nonprime numbers k such that sigma(k) - Sum_{j=1..m}{sigma(k) mod d_j} | k, where d_j is one of the m divisors of k.
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2
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1, 8, 50, 128, 228, 9976, 32768, 41890, 47668, 53064, 501888, 564736, 1207944, 12026888, 14697568, 29720448, 2147483648, 2256502784, 21471264576, 35929849856
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OFFSET
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1,2
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COMMENTS
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For 1, 228, 501888, 1207944, 29720448, etc., being their ratio equal to 1, we have that Sum_{j=1..m}{sigma(k) mod d_j} is the sum of their aliquot parts.
The ratios for the listed terms are 1, 2, 2, 16, 1, 8, 2048, 2, 2, 22, 1, 512, 1, 25976, 32, 1, 67108864, 32768, ...
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LINKS
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EXAMPLE
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sigma(50) = 93; divisors of 50 are 1, 2, 5, 10, 25, 50 and
93 mod 1 + 93 mod 2 + 93 mod 4 + 93 mod 5 + 93 mod 10 + 93 mod 25 + 93 mod 50 = 0 + 1 + 3 + 3 + 18 + 43 = 68 and 50 / (93-68) = 2.
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MAPLE
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with(numtheory): P:=proc(q) local a, b, c, k, n;
for n from 1 to q do if not isprime(n) then a:=sigma(n); b:=sort([op(divisors(n))]);
c:=add(a mod b[k], k=1..nops(b)); if type(n/(a-c), integer) then print(n); fi; fi; od; end: P(10^9);
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PROG
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(PARI) isok(k) = !isprime(k) && !(k % (sigma(k) - sumdiv(k, d, sigma(k) % d))); \\ Michel Marcus, Mar 10 2021
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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