A177355 The number of positive integers m for which the exponents of prime(n) and prime(n+1) in the prime power factorization of m! are both powers of 3.

3, 1, 3, 4, 14, 10, 26, 22, 22, 61, 38, 59, 97, 77, 70, 82, 156

Offset

1,1

Links

Table of n, a(n) for n=1..17.

V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236.

Formula

All such m belong to interval [q, 2*(-1+q^2*(log(2)/(2*log(q)-1)+1))), where q=p_(n+1).

Example

If n=1, then 3<=m<2*(-1+9*(log(2)/(2*log(3)-1)+1))=26.4... In interval [3,26.3) we find only 3 numbers m=3,4,5 with required property. Therefore, a(1)=3.

Crossrefs

Cf. A000142, A177349, A177378, A177436, A177458, A177459, A177498.

Sequence in context: A021323 A284619 A147549 * A349819 A076157 A087493

Adjacent sequences: A177352 A177353 A177354 * A177356 A177357 A177358

Keyword

nonn

Author

Vladimir Shevelev, May 07 2010

Status

approved