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

1,2

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

Links

Table of n, a(n) for n=1..20.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A013002 A012998 A143760 * A356108 A295373 A356746

Adjacent sequences: A064602 A064603 A064604 * A064606 A064607 A064608

Keyword

nonn,more

Author

Labos Elemer, Sep 24 2001

Extensions

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

a(20) from Amiram Eldar, Jan 18 2024

Status

approved