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

1,2

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

Links

Table of n, a(n) for n=1..25.

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A270357 A367787 A108240 * A331711 A223001 A066612

Adjacent sequences: A064603 A064604 A064605 * A064607 A064608 A064609

Keyword

nonn,more

Author

Labos Elemer, Sep 24 2001

Extensions

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

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

Status

approved