A075653 a(n) = n + sopf(n), where sopf is the sum of the distinct prime factors of n (A008472).

1, 4, 6, 6, 10, 11, 14, 10, 12, 17, 22, 17, 26, 23, 23, 18, 34, 23, 38, 27, 31, 35, 46, 29, 30, 41, 30, 37, 58, 40, 62, 34, 47, 53, 47, 41, 74, 59, 55, 47, 82, 54, 86, 57, 53, 71, 94, 53, 56, 57, 71, 67, 106, 59, 71, 65, 79, 89, 118, 70, 122, 95, 73, 66, 83, 82, 134, 87, 95

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

Cf. A008472, A075254, A075255, A076694.

Sequence in context: A276269 A163173 A058640 * A075656 A267573 A345282

Adjacent sequences: A075650 A075651 A075652 * A075654 A075655 A075656

Keyword

easy,nonn

Author

Joseph L. Pe, Oct 11 2002

Status

approved