A369867 a(n) = n * Sum_{p|n, p prime} prime(n/p) / p.

0, 2, 2, 6, 2, 21, 2, 28, 15, 61, 2, 106, 2, 125, 70, 152, 2, 285, 2, 318, 134, 347, 2, 596, 55, 539, 207, 630, 2, 1073, 2, 848, 356, 1009, 174, 1542, 2, 1279, 548, 1572, 2, 2213, 2, 1766, 912, 1915, 2, 2984, 119, 2715, 1018, 2654, 2, 3879, 396, 3148, 1288, 3167

Offset: 1

Author

Wesley Ivan Hurt, Feb 03 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A000040, A351368, A369748, A369749, A369750, A369866.

Cf. A003557, A033286, A246655.

Programs

Mathematica

Table[n*DivisorSum[n, Prime[n/#]/# &, PrimeQ[#] &], {n, 60}]

PARI

a(n) = my(vp=primes([1, n])); n*sum(i=1, #vp, if (!(n % vp[i]), prime(n/vp[i])/vp[i])); \\ Michel Marcus, May 11 2024

Formula

From Wesley Ivan Hurt, May 10 2024: (Start)

a(p^k) = p^(k-1) * prime(p^(k-1)) for primes p and k >= 1.

a(A246655(n)) = A033286(A003557(A246655(n))). (End)