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A318083
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Numbers m such that sigma(sigma(m))/sigma(m) <= sigma(m)/m.
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2
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1, 2, 4, 8, 9, 12, 16, 18, 25, 32, 36, 48, 50, 52, 64, 72, 80, 81, 84, 90, 98, 100, 108, 112, 128, 144, 150, 156, 162, 180, 192, 196, 200, 208, 225, 240, 242, 244, 252, 256, 288, 289, 292, 300, 320, 324, 336, 338, 360, 372, 388, 392, 400, 420, 432, 441, 444, 448, 450, 468, 484
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OFFSET
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1,2
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COMMENTS
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Let g(n) = sigma(n)/n, then f(n) = g(sigma(n))*g(n).
Then this sequence are the integers m for which g(sigma(m)) <= g(m).
Are there other integers than 1, for which sigma(sigma(m))/sigma(m) = sigma(m)/m?
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LINKS
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MATHEMATICA
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q[n_] := Module[{s = DivisorSigma[1, n]}, DivisorSigma[1, s]/s <= s/n]; Select[Range[500], q] (* Amiram Eldar, Apr 04 2024 *)
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PROG
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(PARI) isok(n) = my(sn=sigma(n)); sigma(sn)/sn <= sn/n;
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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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