A063047 Minimum m where (c_n)^m is mutinous (i.e., part of sequence A027854), where c_n is the n-th positive integer not a prime power.

2, 3, 1, 3, 2, 2, 2, 2, 4, 1, 4, 2, 1, 3, 5, 2, 1, 5, 3, 1, 2, 2, 1, 5, 1, 3, 3, 2, 2, 2, 1, 3, 5, 1, 5, 1, 2, 2, 3, 3, 1, 1, 6, 2, 3, 2, 2, 1, 6, 1, 2, 6, 4, 2, 1, 2, 3, 4, 6, 2, 1, 3, 2, 2, 2, 2, 1, 6, 1, 2, 4, 1, 2, 2, 3, 2, 6, 2, 1, 6, 4, 3, 1, 4, 2, 1, 2, 7, 1, 2, 2, 1, 4, 7, 2, 1, 3, 7, 2, 3, 1, 2, 2, 1, 3

Offset

1,1

Comments

Prime powers (p^k, k = nonnegative integer) raised to a power are never mutinous.

Links

Table of n, a(n) for n=1..105.

Formula

m = ceiling[log(p)/(log(c_n) - k log(p))], where p is the largest prime to divide c_n and p^k is the highest power of p to divide c_n.

Example

a(1) = 2 because the first non-prime-power is 6; and 6^2 = 36, but not 6^1, is mutinous.

Crossrefs

Cf. A027854, A024619.

Sequence in context: A072457 A364554 A301630 * A003270 A099054 A071282

Adjacent sequences: A063044 A063045 A063046 * A063048 A063049 A063050

Keyword

nonn

Author

Leroy Quet, Aug 03 2001

Extensions

Definition clarified by Jonathan Sondow, May 18 2014

Status

approved