A091136 Smallest number m such that number of times m divides k! is almost k/n for large k, i.e., smallest m with A090624(m)=n.

1, 2, 3, 8, 5, 32, 7, 128, 25, 512, 11, 2048, 13, 8192, 2187, 32768, 17, 131072, 19, 524288, 121, 2097152, 23, 8388608, 169, 33554432, 1594323, 134217728, 29, 536870912, 31, 2147483648, 289, 8589934592, 129140163, 34359738368, 37

Offset: 0

Author

Henry Bottomley, Dec 19 2003

Keywords

• nonn

Examples

			a(2)=3 noting that 100! is a multiple of 3^48 and 48 is almost 100/2.
		

Crossrefs

Cf. A090622, A090624, A091137.

Formula

a(n) = min_p{p prime and n divisible by p-1} p^(n/(p-1)).

a(p-1) = p.

a(2n+1) = 2^(2n+1).

Smallest divisor of A091137(n) which is not a divisor of A091137(n-1).