A363920 - OEIS

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A363920

a(n) = n^(tpf(n) * dpf(n)), where tpf(n) is the total number of prime factors of n if n >= 2 and otherwise = 0; dpf(n) is the number of distinct prime factors of n if n >= 2 and otherwise = 0.

1, 1, 2, 3, 16, 5, 1296, 7, 512, 81, 10000, 11, 2985984, 13, 38416, 50625, 65536, 17, 34012224, 19, 64000000, 194481, 234256, 23, 110075314176, 625, 456976, 19683, 481890304, 29, 19683000000000, 31, 33554432, 1185921, 1336336, 1500625, 2821109907456, 37, 2085136

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..38.

FORMULA

a(n) = n <=> n term of A000040(n) prepended with 1, n = 1, 2, 3, 5, 7, ...

a(n) != n <=> n term of A002808(n) prepended with 0, n = 0, 4, 6, 8, ...

Moebius(a(n)) = -[n is prime] for n >= 2, where [ ] denotes the Iverson bracket.

MAPLE

with(numtheory):

dpf := n -> ifelse(n = 0, 0, nops(factorset(n))): # dpf = [0] U [A001221].