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

Author

Vladimir Shevelev, May 07 2010

Keywords

• nonn
• more

Examples

			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.
		

Links

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

Crossrefs

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

Formula

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