A337246 Sum of the first coordinates of all pairs of prime divisors of n, (p,q), such that p <= q.

0, 2, 3, 2, 5, 7, 7, 2, 3, 9, 11, 7, 13, 11, 11, 2, 17, 7, 19, 9, 13, 15, 23, 7, 5, 17, 3, 11, 29, 17, 31, 2, 17, 21, 17, 7, 37, 23, 19, 9, 41, 19, 43, 15, 11, 27, 47, 7, 7, 9, 23, 17, 53, 7, 21, 11, 25, 33, 59, 17, 61, 35, 13, 2, 23, 23, 67, 21, 29, 23, 71, 7, 73, 41, 11, 23, 25, 25, 79

Offset: 1

Author

Wesley Ivan Hurt, Aug 20 2020

Keywords

• nonn

Comments

a(n)=n if n is prime. - Robert Israel, Sep 17 2020

Examples

			a(6) = 7; There are 2 prime divisors of 6: {2,3}. If we list all of the ordered pairs (p,q) with p<=q, we get (2,2), (2,3) and (3,3). The sum of the first coordinates from each pair is 2 + 2 + 3 = 7.
a(10) = 9; There are 2 prime divisors of 10: {2,5}. If we list all of the ordered pairs (p,q) with p<=q, we get (2,2), (2,5) and (5,5). The sum of the first coordinates from each pair is 2 + 2 + 5 = 9.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A064939, A337246.

Programs

Maple

f:= proc(n) local F, i,j;
  F:= sort(convert(numtheory:-factorset(n),list),`>`);
  add(i*F[i],i=1..nops(F))
end proc:
map(f, [$1..100]); # Robert Israel, Sep 17 2020

PARI

a(n) = my(vp = factor(n)[,1]~); sum(iq=1, #vp, sum(ip=1, iq, vp[ip])); \\ Michel Marcus, Aug 21 2020

Formula

a(n) = Sum_{p|n, q|n, p and q prime, p<=q} p.