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

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. A001414, A078310, A078314, A078318, A078319.

Programs

Haskell

a078320 = a001414 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

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

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

Formula

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