A078319 - OEIS

A078319

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

2, 5, 7, 3, 15, 37, 7, 17, 9, 101, 63, 73, 24, 197, 115, 14, 36, 109, 183, 70, 32, 102, 60, 34, 12, 677, 43, 134, 423, 70, 52, 18, 116, 102, 615, 38, 144, 22, 763, 401, 31, 358, 44, 39, 15, 102, 37, 17, 45, 170, 1303, 55, 288, 18, 108, 162, 20, 678, 1743, 1801, 1863

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OFFSET

1,1

LINKS

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

FORMULA

a(n) = A008472(A078310(n)).

MATHEMATICA

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

PROG

(PARI) vecprod(v)=prod(i=1, #v, v[i])

rad(n)=vecprod(factor(n)[, 1])