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 A303999 Numbers whose sum of divisors is the seventh power of one of their divisors. 1
 1, 112890, 120054, 124338, 133998, 137058, 139962, 36705396, 39118548, 52166212, 4661585292, 4677211812, 4851457716, 4968055596, 6168611160, 6232929480, 6236525932, 6261521812, 6311227560, 6362855640, 6430524120, 6468862876, 6488003880, 6500134440, 6506266732 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subset of A048257. LINKS EXAMPLE Divisors of 112890 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 71, 106, 142, 159, 213, 265, 318, 355, 426, 530, 710, 795, 1065, 1590, 2130, 3763, 7526, 11289, 18815, 22578, 37630, 56445, 112890 and their sum is 279936 = 6^7. MAPLE with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do a:=sort([op(divisors(n))]); for k from 1 to nops(a) do if sigma(n)=a[k]^7 then print(n); break; fi; od; od; end: P(10^9); MATHEMATICA Select[Range[150000], IntegerQ[t = DivisorSigma[1, #]^(1/7)] && Mod[#, t] == 0 &] (* Giovanni Resta, May 04 2018 *) PROG (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 7) && !(n % sqrtnint(s, 7))); \\ Michel Marcus, May 05 2018 CROSSREFS Cf. A000203, A048257, A303123, A303993, A303994, A303995, A303996. Sequence in context: A269887 A269766 A177275 * A252036 A103113 A179922 Adjacent sequences:  A303996 A303997 A303998 * A304000 A304001 A304002 KEYWORD nonn,easy AUTHOR Paolo P. Lava, May 04 2018 EXTENSIONS a(11)-a(25) from Giovanni Resta, May 04 2018 STATUS approved

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)