A222416 If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention).

1, 2, 3, 4, 5, 5, 7, 8, 9, 7, 11, 7, 13, 9, 8, 16, 17, 11, 19, 9, 10, 13, 23, 11, 25, 15, 27, 11, 29, 10, 31, 32, 14, 19, 12, 13, 37, 21, 16, 13, 41, 12, 43, 15, 14, 25, 47, 19, 49, 27, 20, 17, 53, 29, 16, 15, 22, 31, 59, 12, 61, 33, 16, 64, 18, 16, 67, 21, 26, 14, 71, 17, 73

Offset

1,2

Comments

A variant of A008475, which is the main entry.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Nussbaum, Roger D.; Verduyn Lunel, Sjoerd M., Asymptotic estimates for the periods of periodic points of non-expansive maps, Ergodic Theory Dynam. Systems 23 (2003), no. 4, 1199--1226. See the function S(n). MR1997973 (2004m:37033)

Mathematica

Array[Total[Power @@@ FactorInteger[#]] &, 73] (* Michael De Vlieger, Nov 17 2017 *)

Prog

(PARI)
A008475(n) = { my(f=factor(n)); vecsum(vector(#f~, i, f[i, 1]^f[i, 2])); };
A222416(n) = if(1==n, n, A008475(n)); \\ Antti Karttunen, Nov 17 2017

Crossrefs

Cf. A008475, A222415.

Sequence in context: A340901 A082081 A008475 * A269524 A161656 A306328

Adjacent sequences: A222413 A222414 A222415 * A222417 A222418 A222419

Keyword

nonn

Author

N. J. A. Sloane, Feb 28 2013

Status

approved