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

Author

Antti Karttunen, May 31 2014

Keywords

• nonn

Links

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

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.

Programs

Scheme

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

Formula

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