A210936 Sum of prime factors of prime(n)-1 (counted with multiplicity).

0, 2, 4, 5, 7, 7, 8, 8, 13, 11, 10, 10, 11, 12, 25, 17, 31, 12, 16, 14, 12, 18, 43, 17, 13, 14, 22, 55, 13, 15, 15, 20, 23, 28, 41, 15, 20, 14, 85, 47, 91, 15, 26, 15, 18, 19, 17, 42, 115, 26, 35, 26, 16, 17, 16, 133, 71, 16, 30, 18, 52, 77, 25, 38, 22, 83

Offset: 1

Author

Paolo P. Lava, Mar 30 2012

Keywords

• nonn

Comments

From an idea of Michael B. Porter.

Examples

			prime(10) = 29, and 29-1 = 28 = 2*2*7, so a(10) = 2+2+7 = 11.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023508, A023514, A210934

Programs

Maple

with(numtheory);
P:=proc(i)
local a,k,n;
for n from 1 to i do
  a:=ifactors(ithprime(n)-1)[2]; print(add(a[k][1]*a[k][2],k=1..nops(a)));
od; end:
# alternative
A210936 := proc(n)
        local p,pplus,f ;
        p := ithprime(n) ;
        pplus := ifactors(p-1)[2] ;
        add(op(1,f)*op(2,f),f=pplus) ;
end proc:
seq(A210936(n),n=1..300) ; # R. J. Mathar, May 25 2022

Formula

a(n) = A001414(A006093(n)). - Michel Marcus, Oct 05 2013