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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.
5
3, 1, 3, 4, 14, 10, 26, 22, 22, 61, 38, 59, 97, 77, 70, 82, 156
OFFSET
1,1
LINKS
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.
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 07 2010
STATUS
approved