A320389 Product_i prime(i)^e(i), where e are the nonzero exponents in the prime factorization of n, sorted in increasing order.

1, 2, 2, 4, 2, 6, 2, 8, 4, 6, 2, 18, 2, 6, 6, 16, 2, 18, 2, 18, 6, 6, 2, 54, 4, 6, 8, 18, 2, 30, 2, 32, 6, 6, 6, 36, 2, 6, 6, 54, 2, 30, 2, 18, 18, 6, 2, 162, 4, 18, 6, 18, 2, 54, 6, 54, 6, 6, 2, 150, 2, 6, 18, 64, 6, 30, 2, 18, 6, 30, 2, 108, 2, 6, 18, 18

Offset

1,2

Comments

Here the exponents are sorted in increasing order; if they are sorted in decreasing order, we get A046523: the smallest number with the same prime signature as n.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Maple

a:= n-> (l-> mul(ithprime(i)^l[i], i=1..nops(l)))(
             sort(map(i-> i[2], ifactors(n)[2]))):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 18 2020

Prog

(PARI) a(n)=factorback(matconcat([primes(#n=factor(n)[, 2])~, vecsort(n)]))

Crossrefs

Cf. A046523.

Sequence in context: A347458 A107067 A331580 * A378447 A046801 A348717

Adjacent sequences: A320386 A320387 A320388 * A320390 A320391 A320392

Keyword

nonn

Author

M. F. Hasler, Oct 12 2018

Status

approved