A240764 Least k such that prime power factorization of A240751(k)! contains p^k when the smallest such p equals prime(n), or a(n)=0 if there is no such k.

1, 2, 12, 29, 186, 2865, 3265, 379852, 7172525

Offset

1,2

Comments

The first position k in A240755 in which A240755(k) = prime(n), or a(n)=0 if prime(n) does not occur in A240755.

Conjecture: all a(n)>0.

Links

Table of n, a(n) for n=1..9.

David A. Corneth, A240751; a(n) is the smallest k such that in the prime power factorization of k! there exists at least one exponent n., Seqfan, (Mar 25 2017)

Example

A240751(a(3))! = A240751(12)! = 50!. 50! is the least factorial having exponent 12 in its prime factorization. That exponent denotes the multiplicity of prime(3) = 5. - David A. Corneth, Mar 27 2017

Crossrefs

Cf. A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672, A240695, A240751, A240755.

Sequence in context: A345694 A326517 A248119 * A215784 A061780 A249411

Adjacent sequences: A240761 A240762 A240763 * A240765 A240766 A240767

Keyword

nonn,more

Author

Vladimir Shevelev, Apr 12 2014

Extensions

a(5)-a(7) from Peter J. C. Moses, Apr 14 2014

a(8)-a(9) from David A. Corneth, Mar 27 2017

Status

approved