A078320 - OEIS

A078320

Sum of all prime factors of n*rad(n)+1, where rad = A007947 (squarefree kernel).

2, 5, 7, 6, 15, 37, 12, 17, 11, 101, 63, 73, 24, 197, 115, 14, 36, 109, 183, 70, 32, 102, 60, 34, 15, 677, 43, 134, 423, 70, 52, 18, 116, 102, 615, 38, 144, 39, 763, 401, 60, 358, 49, 39, 30, 102, 37, 34, 49, 170, 1303, 55, 288, 23, 108, 162, 30, 678, 1743, 1801

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001414(A078310(n)).

MATHEMATICA

a[n_] := Plus @@ Times @@@ FactorInteger[1 + n * Times @@ FactorInteger[n][[;; , 1]]]; Array[a, 100] (* Amiram Eldar, Apr 10 2025 *)

PROG

(PARI) rad(n)=my(f=factor(n)[, 1]); prod(i=1, #f, f[i])

a(n)=my(f=factor(n*rad(n)+1)); sum(i=1, #f~, f[i, 1]*f[i, 2]) \\ Charles R Greathouse IV, Jul 15 2013