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

1,1

Comments

108927 is the smallest odd term of this sequence.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000203, A001065, A007947, A027598.

Sequence in context: A328375 A141717 A185742 * A181702 A304890 A264155

Adjacent sequences: A286873 A286874 A286875 * A286877 A286878 A286879

Keyword

nonn

Author

Altug Alkan, Aug 02 2017

Status

approved