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 A304000 Numbers whose sum of divisors is the eighth power of one of their divisors. 0
 1, 600270, 621690, 669990, 685290, 693294, 699810, 725934, 774894, 782598, 813378, 823938, 839802, 508541124, 553420812, 678160756, 127444892484, 130213538364, 131470441284, 131515433868, 131523414204, 131528229924, 137156770884, 139602234324, 140161757484 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subset of A048258. If m and n are coprime members of the sequence, then m*n is in the sequence. However, it is not clear whether there are such m and n where neither is 1: in particular, are there odd members other than 1? - Robert Israel, May 10 2018 LINKS Table of n, a(n) for n=1..25. EXAMPLE Divisors of 600270 are 1, 2, 3, 5, 6, 10, 11, 15, 17, 22, 30, 33, 34, 51, 55, 66, 85, 102, 107, 110, 165, 170, 187, 214, 255, 321, 330, 374, 510, 535, 561, 642, 935, 1070, 1122, 1177, 1605, 1819, 1870, 2354, 2805, 3210, 3531, 3638, 5457, 5610, 5885, 7062, 9095, 10914, 11770, 17655, 18190, 20009, 27285, 35310, 40018, 54570, 60027, 100045, 120054, 200090, 300135, 600270 and their sum is 1679616 = 6^8. 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]^8 then print(n); break; fi; od; od; end: P(10^9); PROG (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 8) && !(n % sqrtnint(s, 8))); \\ Michel Marcus, May 05 2018 CROSSREFS Cf. A000203, A048258, A303123, A303993, A303994, A303995, A303996, A303999. Sequence in context: A209515 A106779 A106780 * A206412 A235257 A185928 Adjacent sequences: A303997 A303998 A303999 * A304001 A304002 A304003 KEYWORD nonn AUTHOR Paolo P. Lava, May 04 2018 EXTENSIONS a(17)-a(25) from Giovanni Resta, May 04 2018 STATUS approved

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Last modified July 15 18:49 EDT 2024. Contains 374333 sequences. (Running on oeis4.)