A286876 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.

24, 40, 216, 234, 360, 588, 2016, 3724, 4320, 4680, 6048, 6552, 9720, 11466, 22932, 54432, 58752, 97920, 99200, 108927, 137214, 167580, 185562, 217854, 297600, 309582, 435708, 448335, 524160, 544635, 637000, 804384, 871416, 931840, 1284192, 1384110, 1489752

Offset: 1

Author

Altug Alkan, Aug 02 2017

Keywords

• nonn

Comments

108927 is the smallest odd term of this sequence.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000203, A001065, A007947, A027598.

Programs

Mathematica

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 *)

PARI

rad(n) = factorback(factorint(n)[, 1]);
isok(n) = rad(sigma(n)-n)==rad(n) && rad(sigma(n))!=rad(n);