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6, 28, 110, 496, 884, 8128, 18632, 85936, 116624, 15370304, 33550336, 73995392, 815634435, 3915380170, 5556840416, 6800695312, 8589869056
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OFFSET
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1,1
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COMMENTS
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No further terms below 2^31.
The quotients A000120(k)/(sigma(k)-A005187(k)) for these terms are: 1, 1, 5, 1, 3, 1, 5, 9, 2, 2, 1, 2, 2. Ones occur at the positions of perfect numbers.
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LINKS
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EXAMPLE
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110 is "1101110" in binary, thus A000120(110) = 5. Sigma(110) = 216, while A005187(110) = 215, thus as 5 = 5*(216-215), 110 is included in this sequence.
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MATHEMATICA
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q[n_] := Module[{bw = DigitCount[n, 2, 1], ab = DivisorSigma[1, n] - 2*n, sum}, (sum = ab + bw) > 0 && Divisible[bw, sum]]; Select[Range[10^5], q] (* Amiram Eldar, Jan 03 2021 *)
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PROG
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(PARI)
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
isA326131(n) = { my(t=sigma(n)-A005187(n)); (gcd(hammingweight(n), t) == t); };
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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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