A064606 Numbers k such that A064603(k) is divisible by k.

1, 2, 7, 45, 184, 210, 267, 732, 1282, 3487, 98374, 137620, 159597, 645174, 3949726, 7867343, 13215333, 14153570, 14262845, 317186286, 337222295, 2788845412, 10937683400, 72836157215, 95250594634

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(22) > 2*10^9. - Donovan Johnson, Jun 21 2010

a(26) > 10^11, if it exists. - Amiram Eldar, Jan 18 2024

Examples

			Adding divisor-cube sums for j = 1..7 gives 1+9+28+73+126+252+344 = 833 = 7*119, which is divisible by 7, so 7 is a term and the integer quotient is 119.
		

Crossrefs

Cf. A001158, A064603, A050226, A056650, A064605, A064607, A064610-A064612, A048290, A062982, A045345.

Programs

Mathematica

A064603 = Accumulate[Table[DivisorSigma[3, k], {k, 1, 1000000}]]; Select[Range[Length[A064603]], Divisible[A064603[[#]], #] &] (* Vaclav Kotesovec, Jul 11 2021 *)

Formula

(Sum_{j=1..k} sigma_3(j)) mod k = A064603(k) mod k = 0.

Extensions

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

a(22)-a(25) from Amiram Eldar, Jan 18 2024