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

1,2

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

Links

Table of n, a(n) for n=1..23.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A062617 A376470 A207139 * A182974 A005345 A174366

Adjacent sequences: A064604 A064605 A064606 * A064608 A064609 A064610

Keyword

nonn,more

Author

Labos Elemer, Sep 24 2001

Extensions

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

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

Status

approved