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 A289384 Numbers k such that the sum of the divisors of k is of the form m^3 + 1. 1
 1, 12, 68, 82, 100, 730, 886, 1089, 1241, 1252, 1352, 1440, 1908, 2804, 2947, 3274, 5598, 6078, 7414, 9123, 10135, 10164, 10804, 10809, 11143, 12756, 13456, 13468, 15004, 21025, 23810, 24642, 25123, 26912, 26983, 34976, 37020, 40477, 45946, 48126, 55964, 56764 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Perfect squares in the sequence are 1, 100, 1089, 13456, 21025, ... LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..1510 EXAMPLE 730 is in the sequence because sigma(730) = 1332 = 11^3 + 1. MAPLE a:= proc(n) option remember; local k; for k from 1+`if`(n=1, 0, a(n-1)) while (t->t<> iroot(t, 3)^3)(numtheory[sigma](k)-1) do od; k end: seq(a(n), n=1..40); # Alois P. Heinz, Jul 04 2017 MATHEMATICA fQ[n_] := ! PrimeQ@n && Block[{sd = DivisorSigma[1, n]}, IntegerQ[(sd - 1)^(1/3)]]; Select[Range@59323, fQ] (* Robert G. Wilson v, Jul 05 2017 *) PROG (PARI) isok(n) = ispower(sigma(n)-1, 3); \\ Michel Marcus, Jul 05 2017 CROSSREFS Cf. A000203, A001093, A289290. Sequence in context: A117088 A199415 A200204 * A200205 A059585 A213547 Adjacent sequences: A289381 A289382 A289383 * A289385 A289386 A289387 KEYWORD nonn AUTHOR Michel Lagneau, Jul 04 2017 EXTENSIONS More terms from Alois P. Heinz, Jul 04 2017 STATUS approved

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Last modified September 8 12:12 EDT 2024. Contains 375753 sequences. (Running on oeis4.)