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A064606 Numbers k such that A064603(k) is divisible by k. 9
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A270357 A367787 A108240 * A331711 A223001 A066612
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

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Last modified March 28 07:46 EDT 2024. Contains 371235 sequences. (Running on oeis4.)