A064605 Numbers k such that A064602(k) is divisible by k.

1, 2, 8, 74, 146, 150, 158, 307, 526, 541, 16157, 20289, 271343, 953614, 1002122, 2233204, 3015123, 15988923, 48033767, 85110518238

Offset: 1

Author

Labos Elemer, Sep 24 2001

Keywords

• nonn
• more

Comments

Analogous sequences for various arithmetical functions are A050226, A056650, A064605, A064606, A064607, A064610, A064611, A048290, A062982, A045345.

a(20) > 3*10^10. - Donovan Johnson, Aug 31 2012

a(21) > 10^11, if it exists. - Amiram Eldar, Jan 18 2024

Examples

			Summing divisor-square sums for j = 1..8 gives 1+5+10+21+26+50+50+85 = 248, which is divisible by 8, so 8 is a term and the integer quotient is 31.
		

Crossrefs

Cf. A001157, A064602, A050226, A056650, A064606, A064607, A064610, A064611, A064612, A048290, A062982, A045345.

Programs

Mathematica

k = 1; lst = {}; s = 0; While[k < 1000000001, s = s + DivisorSigma[2, k]; If[ Mod[s, k] == 0, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Apr 25 2011 *)

Formula

(Sum_{j=1..k} sigma_2(j)) mod k = A064602(k) mod k = 0.

Extensions

a(15)-a(19) from Donovan Johnson, Jun 21 2010

a(20) from Amiram Eldar, Jan 18 2024