OFFSET
1,2
COMMENTS
For 1 <= k <= n, add sigma(k) if k is a prime factor of n, otherwise add 1. For example, a(6) = 11 since for k = 1,2,.. we have 1 + sigma(2) + sigma(3) + 1 + 1 + 1 = 1 + (1+2) + (1+3) + 1 + 1 + 1 = 11. - Wesley Ivan Hurt, Oct 18 2021
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n + A008472(n).
a(p) = 2p for primes p. - Wesley Ivan Hurt, Oct 18 2021
EXAMPLE
6 + sum of prime factors of 6 = 6 + 2 + 3 = 11, so a(6) = 11.
MATHEMATICA
Flatten[Append[{1}, Table[n + Apply[Plus, Transpose[FactorInteger[n]][[1]]], {n, 2, 100}]]]
Join[{1}, Table[n+Total[FactorInteger[n][[All, 1]]], {n, 2, 70}]] (* Harvey P. Dale, Sep 29 2016 *)
PROG
(PARI) a(n) = n + vecsum(factor(n)[, 1]); \\ Michel Marcus, Feb 22 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Oct 11 2002
STATUS
approved