A344732 Numbers k such that k divides Sum_{j=1..k} A048105(j).

1, 2, 3, 54, 58, 62, 71, 10535, 10541, 10579, 135242, 135243, 1733777, 1733781, 1733895, 1733905, 1733999, 22216757, 22216765, 22216790, 22216808, 22216814, 46745561148, 46745561156

Offset

1,2

Comments

The corresponding quotients Sum_{j=1..k} A048105(j)/k are 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 9, 9, ...

a(25) > 7.5*10^10, if it exists.

Links

Table of n, a(n) for n=1..24.

Example

a(1) = 1 since A048105(1) = 0 is divisible by 1.
a(4) = 54 since Sum_{j=1..54} A048105(j) = 54 is divisible by 54.

Mathematica

s[1] = 0; s[n_] := s[n] = s[n - 1] + DivisorSigma[0, n] - 2^PrimeNu[n]; Select[Range[140000], Divisible[s[#], #] &]

Crossrefs

Cf. A048105.

The non-unitary version of A050226.

Similar sequences: A064610, A344731, A344733.

Sequence in context: A342408 A062641 A339920 * A037424 A155088 A072871

Adjacent sequences: A344729 A344730 A344731 * A344733 A344734 A344735

Keyword

nonn,more

Author

Amiram Eldar, May 27 2021

Status

approved