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A240073
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Deficient numbers k for which sigma(k), the sum of divisors of k, reaches a new maximum.
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1
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1, 2, 3, 4, 7, 8, 10, 14, 16, 21, 22, 26, 32, 44, 50, 52, 63, 64, 76, 92, 98, 105, 110, 124, 128, 136, 152, 170, 182, 184, 212, 225, 230, 232, 248, 256, 290, 296, 310, 315, 328, 344, 370, 376, 405, 410, 424, 470, 472, 484, 495, 512, 568, 584, 592, 632, 656
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OFFSET
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1,2
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COMMENTS
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Every power of 2 appears. The deficient number k has sigma(k) < 2*k. In relation to the highly abundant numbers, these numbers might be termed highly deficient numbers.
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LINKS
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MATHEMATICA
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t = {}; mn = 0; n = 0; While[Length[t] < 100, n++; d = DivisorSigma[1, n]; If[mn < d < 2*n, AppendTo[t, n]; mn = d]]; t
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PROG
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(PARI) lista(kmax) = {my(sigmax = 0, sig); for(k = 1, kmax, sig = sigma(k); if(sig < 2*k && sig > sigmax, sigmax = sig; print1(k, ", "))); } \\ Amiram Eldar, Apr 06 2024
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CROSSREFS
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Cf. A228450 (deficient numbers with increasing abundancy).
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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