A249338 Sum of prime indices in the prime factorization of A249336(n), counted with multiplicity: a(n) = A056239(A249336(n)).

0, 0, 1, 0, 2, 0, 2, 1, 1, 2, 2, 2, 3, 0, 3, 1, 2, 3, 2, 4, 0, 3, 2, 3, 3, 3, 4, 1, 3, 3, 4, 2, 4, 2, 4, 3, 4, 3, 5, 0, 4, 4, 3, 4, 4, 4, 5, 1, 3, 6, 0, 3, 5, 2, 5, 2, 4, 4, 6, 1, 4, 5, 3, 5, 3, 4, 5, 4, 4, 7, 0, 4, 5, 3, 7, 1, 3, 5, 4, 8, 0, 4, 5, 4, 6, 2, 6, 2, 5, 5, 4, 6, 3, 8, 1, 4, 9, 0

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..12580

Formula

a(n) = A056239(A249336(n)).

Other identities. For all n >= 1:

a(A249339(n)) = 0.

a(A249340(n)) = n-1. [A249340 gives the positions of records (just before each zero) that are consecutive nonnegative integers, A001477.]

Prog

(PARI)
A049084(n) = if(isprime(n), primepi(n), 0); \\ This function from Charles R Greathouse IV
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * A049084(f[i, 1]))); }
A249338_write_bfile(up_to_n) = { my(counts, n, a_k, a_n); counts = vector(up_to_n); a_k = 1; for(n = 1, up_to_n, a_n = A056239(a_k); write("b249338_upto12580.txt", n, " ", a_n); counts[1+a_n]++; a_k = counts[1+a_n]); };
A249338_write_bfile(12580);
(Scheme) (define (A249338 n) (A056239 (A249336 n)))

Crossrefs

Cf. A001477, A056239, A249336, A249339 (positions of zeros), A249340 (positions of records), A249072.

Sequence in context: A000586 A029399 A302172 * A046069 A320042 A055651

Adjacent sequences: A249335 A249336 A249337 * A249339 A249340 A249341

Keyword

nonn

Author

Antti Karttunen, Oct 26 2014

Status

approved