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A046870
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Numbers k such that sigma_1(k) divides sigma_4(k).
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2
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1, 4, 9, 16, 20, 25, 36, 49, 50, 64, 81, 100, 117, 121, 144, 169, 180, 196, 225, 242, 256, 289, 324, 325, 361, 400, 441, 450, 468, 484, 500, 529, 576, 578, 605, 625, 650, 676, 729, 784, 800, 841, 900, 961, 980, 1024, 1025, 1058, 1089, 1156, 1225, 1280, 1296
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OFFSET
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1,2
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COMMENTS
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sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).
sigma_2(n) is the sum of the squares of the divisors of n (A001157).
sigma_4(n) is the sum of the 4th powers of the divisors of n (A001159).
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LINKS
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EXAMPLE
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k = a(18) = 196 of which divisor power sums for k=0,1,2,3,4 are 9,399,51471, 8613489, 1574446419. sigma_1(k) = 399 and sigma_4(k) = 51471*30589=399*129*30589. Thus both sigma_2(k) and sigma_1(k) divide sigma_4(k).
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MATHEMATICA
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Select[Range[1300], Divisible @@ DivisorSigma[{4, 1}, #] &] (* Amiram Eldar, Jun 15 2024 *)
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PROG
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(PARI) is(k) = {my(f = factor(k)); !(sigma(f, 4) % sigma(f)); } \\ Amiram Eldar, Jun 15 2024
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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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