A210934 Sum of prime factors of prime(n)+1 (counted with multiplicity).

3, 4, 5, 6, 7, 9, 8, 9, 9, 10, 10, 21, 12, 15, 11, 11, 12, 33, 21, 12, 39, 13, 14, 13, 16, 22, 19, 13, 18, 24, 14, 18, 28, 16, 15, 25, 81, 45, 16, 34, 15, 22, 15, 99, 19, 16, 57, 17, 26, 30, 21, 16, 24, 17, 48, 20, 16, 25, 141, 52, 75, 19, 22, 22, 159, 58, 87

Offset

1,1

Comments

From an idea of Michael B. Porter.

Links

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

Formula

a(n) = A001414(A008864(n)). - Michel Marcus, Oct 05 2013

Example

prime(8) = 19, and 19+1 = 20 = 2*2*5, so a(8) = 2+2+5 = 9.

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
A210934 := 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(A210934(n), n=1..300) ; # R. J. Mathar, May 25 2022

Crossrefs

Cf. A023508, A023514, A210936

Sequence in context: A037350 A014615 A144046 * A354774 A194276 A184336

Adjacent sequences: A210931 A210932 A210933 * A210935 A210936 A210937

Keyword

nonn

Author

Paolo P. Lava, Mar 30 2012

Status

approved