A286876 - OEIS

%I #19 May 10 2020 02:51:53

%S 24,40,216,234,360,588,2016,3724,4320,4680,6048,6552,9720,11466,22932,

%T 54432,58752,97920,99200,108927,137214,167580,185562,217854,297600,

%U 309582,435708,448335,524160,544635,637000,804384,871416,931840,1284192,1384110,1489752

%N Numbers n such that the set of prime divisors of n is equal to the set of prime divisors of sum of proper divisors of n while n is not in A027598.

%C 108927 is the smallest odd term of this sequence.

%H Amiram Eldar, <a href="/A286876/b286876.txt">Table of n, a(n) for n = 1..100</a>

%e 24 is in the sequence because 24 = 2^3*3 and sum of proper divisors of 24 is 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36 = 2^2*3^2 while sigma(24) = 60 is divisible by 5.

%t Select[Range[1500000], And[UnsameQ @@ {#1, #2}, SameQ @@ {#1, #3}] & @@ Map[FactorInteger[#][[All, 1]] &, {#1, #2, #2 - #1} & @@ {#, DivisorSigma[1, #]}] &] (* _Michael De Vlieger_, Aug 02 2017 *)

%o (PARI) rad(n) = factorback(factorint(n)[, 1]);

%o isok(n) = rad(sigma(n)-n)==rad(n) && rad(sigma(n))!=rad(n);

%Y Cf. A000203, A001065, A007947, A027598.

%K nonn

%O 1,1

%A _Altug Alkan_, Aug 02 2017