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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.
2
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Aug 02 2017
STATUS
approved