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

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A007947, A008472, A078310, A078313, A078318, A078320.

Programs

Haskell

a078319 = a008472 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

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

PARI

vecprod(v)=prod(i=1,#v,v[i])
rad(n)=vecprod(factor(n)[,1])
a(n)=vecsum(factor(n*rad(n)+1)[,1]) \\ Charles R Greathouse IV, Jul 09 2013

Formula

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