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 A303995 Numbers whose sum of divisors is the fifth power of one of their divisors. 6
 1, 3210, 3498, 3882, 6453804, 7873684, 7943640, 8028120, 8099880, 9112230, 9561990, 10079430, 182626920, 192651480, 196192920, 199939320, 200271960, 201632760, 203289240, 206367480, 206645880, 207815160, 208955160, 210368760, 210406680, 210717720, 211645560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subset of A019423. LINKS Table of n, a(n) for n=1..27. EXAMPLE Divisors of 3210 are 1, 2, 3, 5, 6, 10, 15, 30, 107, 214, 321, 535, 642, 1070, 1605, 3210 and their sum is 7776 = 6^5. 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]^5 then print(n); break; fi; od; od; end: P(10^9); MATHEMATICA Select[Range[10^4], IntegerQ[t = DivisorSigma[1, #]^(1/5)] && Mod[#, t] == 0 &] (* Giovanni Resta, May 04 2018 *) PROG (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 5) && !(n % sqrtnint(s, 5))); \\ Michel Marcus, May 05 2018 CROSSREFS Cf. A000203, A019423, A303123, A303993, A303994, A303996. Sequence in context: A236252 A232262 A048255 * A091329 A261241 A345772 Adjacent sequences: A303992 A303993 A303994 * A303996 A303997 A303998 KEYWORD nonn AUTHOR Paolo P. Lava, May 04 2018 EXTENSIONS a(13)-a(27) from Giovanni Resta, May 04 2018 STATUS approved

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Last modified June 12 10:35 EDT 2024. Contains 373331 sequences. (Running on oeis4.)