A064610 Places k where A064608(k) (partial sums of unitary tau) is divisible by k.

1, 35, 37, 1015, 27417, 27421, 27449, 27453, 19774739, 530743781, 530743799, 530743807, 530743813

Offset: 1

Author

Labos Elemer, Sep 24 2001

Keywords

• nonn
• more

Comments

The corresponding quotients are 1, 3, 3, 5, 7, 7, 7, 7, 11, 13, 13, 13, 13, ...

a(14) > 7.5*10^10, if it exists. - Amiram Eldar, Jun 04 2021

Examples

			For n = 37, the sum A064608(37) = 1+2+2+2+2+4+2+...+4+4+4+2 = 111 = 3*37, so 37 is in the sequence.
		

Crossrefs

Cf. A064608.

Analogous "integer-mean" sequences for various arithmetical functions are A050226, A056650, A064605, A064606, A064607, A048290, A063986, A063971, A064911, A062982, A045345.

Programs

Mathematica

s[1] = 1; s[n_] := s[n] = s[n - 1] + 2^PrimeNu[n]; Select[Range[30000], Divisible[s[#], #] &] (* Amiram Eldar, Jun 04 2021 *)

Formula

{n: A064608(n) == 0 (mod n)}.

Extensions

a(10)-a(13) from Donovan Johnson, Jul 20 2012