A063047 - OEIS

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

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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