cp's OEIS Frontend

A304000 Numbers whose sum of divisors is the eighth power of one of their divisors.

%I A304000 #16 May 11 2018 06:08:34
%S A304000 1,600270,621690,669990,685290,693294,699810,725934,774894,782598,
%T A304000 813378,823938,839802,508541124,553420812,678160756,127444892484,
%U A304000 130213538364,131470441284,131515433868,131523414204,131528229924,137156770884,139602234324,140161757484
%N A304000 Numbers whose sum of divisors is the eighth power of one of their divisors.
%C A304000 Subset of A048258.
%C A304000 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
%e A304000 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.
%p A304000 with(numtheory): P:=proc(q) local a,k,n;
%p A304000 for n from 1 to q do a:=sort([op(divisors(n))]);
%p A304000 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);
%o A304000 (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 8) && !(n % sqrtnint(s, 8))); \\ _Michel Marcus_, May 05 2018
%Y A304000 Cf. A000203, A048258, A303123, A303993, A303994, A303995, A303996, A303999.
%K A304000 nonn
%O A304000 1,2
%A A304000 _Paolo P. Lava_, May 04 2018
%E A304000 a(17)-a(25) from _Giovanni Resta_, May 04 2018