A190125 If n = product(p_i^e_i), a(n) = product((p_i^e_i)^(p_i^e_i)).

1, 4, 27, 256, 3125, 108, 823543, 16777216, 387420489, 12500, 285311670611, 6912, 302875106592253, 3294172, 84375, 18446744073709551616, 827240261886336764177, 1549681956, 1978419655660313589123979, 800000, 22235661, 1141246682444

Offset

1,2

Comments

Multiplicative with a(p^e) = (p^e)^(p^e) = p^(e*p^e).

Equivalently, product over pp a unitary prime power divisor of n of pp^pp.

Links

Table of n, a(n) for n=1..22.

Prog

(PARI) a(n)=local(fm, pp); fm=factor(n); prod(k=1, matsize(fm)[1], (pp=fm[k, 1]^fm[k, 2])^pp)

Crossrefs

Cf. A133482.

Sequence in context: A365095 A324804 A245409 * A324805 A245410 A324806

Adjacent sequences: A190122 A190123 A190124 * A190126 A190127 A190128

Keyword

nonn,mult

Author

Franklin T. Adams-Watters, May 05 2011

Status

approved