A082666 - OEIS

A082666

a(1) = 0, for n > 1 if n = prime(k), then a(n) = k, otherwise a(n) = Sum_{d|n, d<n} a(d).

0, 1, 2, 1, 3, 3, 4, 2, 2, 4, 5, 7, 6, 5, 5, 4, 7, 8, 8, 9, 6, 6, 9, 16, 3, 7, 4, 11, 10, 18, 11, 8, 7, 8, 7, 24, 12, 9, 8, 20, 13, 21, 14, 13, 12, 10, 15, 36, 4, 11, 9, 15, 16, 20, 8, 24, 10, 11, 17, 53, 18, 12, 14, 16, 9, 24, 19, 17, 11, 24, 20, 66, 21, 13, 13

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..75.

FORMULA

a(1) = 0, a(n) = A049084(n) + Sum_{d|n, d<n} a(d) for n > 1.

EXAMPLE

a(20) = a(1) + a(2) + a(4) + a(5) + a(10) = 0 + 1 + (a(1)+a(2)) + 3 + (a(1)+a(2)+a(5)) = 0 + 1 + (0+1) + 3 + (0+1+3) = 1 + 1 + 3 + 4 = 9.

PROG

(PARI) lista(nn) = {my(v=vector(nn)); for(n=2, nn, v[n]=if(isprime(n), primepi(n), sumdiv(n, d, v[d]))); v; } \\ Jinyuan Wang, Apr 07 2020

CROSSREFS