A248151 Numbers n such that the sum of the divisors of n is not divisible by 4.

1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, 34, 36, 37, 40, 41, 45, 49, 50, 52, 53, 58, 61, 64, 68, 72, 73, 74, 80, 81, 82, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 121, 122, 128, 136, 137, 144, 146, 148, 149, 153, 157, 160, 162, 164, 169, 173, 178, 180

Offset: 1

Author

M. F. Hasler, Oct 02 2014

Keywords

• nonn

Comments

The complement of A248150; contains in particular A028982, the squares and twice the squares, for which sigma is odd.

The terms cannot have more than one odd prime factor to an odd power. Therefore this set has asymptotic density zero. The sequence grows faster than .75 n log(n). In particular: a(10) = 17, a(100) = 298, a(10^3) = 4724, a(10^4) = 66533, a(10^5) = 872434, a(10^6) = 10819205. - M. F. Hasler, Apr 26 2017

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203 (sum of divisors), A028982, A028983, A248150.

Subsequence of A285801.

Programs

Mathematica

Select[Range[200],Mod[DivisorSigma[1,#],4]!=0&] (* Harvey P. Dale, Apr 03 2025 *)

PARI

for(n=1,999,sigma(n)%4&&print1(n","))