A304000 - OEIS

%I #16 May 11 2018 06:08:34

%S 1,600270,621690,669990,685290,693294,699810,725934,774894,782598,

%T 813378,823938,839802,508541124,553420812,678160756,127444892484,

%U 130213538364,131470441284,131515433868,131523414204,131528229924,137156770884,139602234324,140161757484

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

%C Subset of A048258.

%C 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 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 with(numtheory): P:=proc(q) local a,k,n;

%p for n from 1 to q do a:=sort([op(divisors(n))]);

%p 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 (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 8) && !(n % sqrtnint(s, 8))); \\ _Michel Marcus_, May 05 2018

%Y Cf. A000203, A048258, A303123, A303993, A303994, A303995, A303996, A303999.

%K nonn

%O 1,2

%A _Paolo P. Lava_, May 04 2018

%E a(17)-a(25) from _Giovanni Resta_, May 04 2018