A297173 Smallest difference between indices of prime divisors of n, or 0 if n is a prime power.

0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 3, 1, 0, 0, 1, 0, 2, 2, 4, 0, 1, 0, 5, 0, 3, 0, 1, 0, 0, 3, 6, 1, 1, 0, 7, 4, 2, 0, 1, 0, 4, 1, 8, 0, 1, 0, 2, 5, 5, 0, 1, 2, 3, 6, 9, 0, 1, 0, 10, 2, 0, 3, 1, 0, 6, 7, 1, 0, 1, 0, 11, 1, 7, 1, 1, 0, 2, 0, 12, 0, 1, 4, 13, 8, 4, 0, 1, 2, 8, 9, 14, 5, 1, 0, 3, 3, 2, 0, 1, 0, 5, 1

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Formula

a(A073491(n)) <= 1.

Example

For n = 130 = 2*5*13 = prime(1)*prime(3)*prime(6), the smallest difference between indices is 3-1 = 2, thus a(130) = 2.

Prog

(PARI) A297173(n) = if(omega(n)<=1, 0, my(ps=factor(n)[, 1]); vecmin(vector((#ps)-1, i, primepi(ps[i+1])-primepi(ps[i]))));

Crossrefs

Cf. A000720, A073490, A073491.

Cf. also A100573, A243055, A242411, A261079, A286470, A286471.

Sequence in context: A124305 A349395 A087073 * A242411 A286470 A243055

Adjacent sequences: A297170 A297171 A297172 * A297174 A297175 A297176

Keyword

nonn

Author

Antti Karttunen, Mar 03 2018

Status

approved