A064607 Numbers k such that A064604(k) is divisible by k.

1, 2, 7, 151, 257, 1823, 3048, 5588, 6875, 7201, 8973, 24099, 5249801, 9177919, 18926164, 70079434, 78647747, 705686794, 2530414370, 3557744074, 25364328389, 32487653727, 66843959963

Offset: 1

Author

Labos Elemer, Sep 24 2001

Keywords

• nonn
• more

Comments

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

a(19) > 2*10^9. - Donovan Johnson, Jun 21 2010

a(24) > 10^11, if it exists. - Amiram Eldar, Jan 18 2024

Examples

			Adding 4th-power divisor-sums for j = 1..7 gives 1+17+82+273+626+1394+2402 = 4795 which is divisible by 7, so 7 is a term and the integer quotient is 655.
		

Crossrefs

Cf. A001159, A064604, A050226, A056650, A064605, A064606, A064610-A064612, A048290, A062982, A045345.

Programs

Mathematica

k = 1; lst = {}; s = 0; While[k < 1000000001, s = s + DivisorSigma[4, k]; If[ Mod[s, k] == 0, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G.Wilson v, Aug 25 2011 *)

Formula

(Sum_{j=1..k} sigma_4(j)) mod k = A064604(k) mod k = 0.

Extensions

a(13)-a(18) from Donovan Johnson, Jun 21 2010

a(19)-a(23) from Amiram Eldar, Jan 18 2024