A243056 If n is the i-th prime, p_i = A000040(i), then a(n) = i, otherwise the difference between the indices of the smallest and the largest prime dividing n: for n = p_i * ... * p_k, where p_i <= ... <= p_k, a(n) = (k-i); a(1) = 0 by convention.

0, 1, 2, 0, 3, 1, 4, 0, 0, 2, 5, 1, 6, 3, 1, 0, 7, 1, 8, 2, 2, 4, 9, 1, 0, 5, 0, 3, 10, 2, 11, 0, 3, 6, 1, 1, 12, 7, 4, 2, 13, 3, 14, 4, 1, 8, 15, 1, 0, 2, 5, 5, 16, 1, 2, 3, 6, 9, 17, 2, 18, 10, 2, 0, 3, 4, 19, 6, 7, 3, 20, 1, 21, 11, 1, 7, 1, 5, 22, 2, 0, 12, 23, 3, 4, 13, 8, 4, 24, 2

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(1) = 0, for n>1, if n = A000040(i), a(n) = i, otherwise a(n) = A061395(n) - A055396(n) = A243055(n).

Prog

(Scheme) (define (A243056 n) (if (prime? n) (A049084 n) (A243055 n)))

Crossrefs

Useful when computing A243057 or A243059.

A025475 (prime powers that are not primes) gives the positions of zeros.

Differs from A241917 for the first time at n=18.

Cf. A243055, A241919, A242411, A049084, A027748, A055396, A061395.

Sequence in context: A355525 A241917 A355526 * A338568 A377734 A279119

Adjacent sequences: A243053 A243054 A243055 * A243057 A243058 A243059

Keyword

nonn

Author

Antti Karttunen, May 31 2014

Status

approved