A359600 The least odd number with the same prime signature as n.

1, 3, 3, 9, 3, 15, 3, 27, 9, 15, 3, 45, 3, 15, 15, 81, 3, 45, 3, 45, 15, 15, 3, 135, 9, 15, 27, 45, 3, 105, 3, 243, 15, 15, 15, 225, 3, 15, 15, 135, 3, 105, 3, 45, 45, 15, 3, 405, 9, 45, 15, 45, 3, 135, 15, 135, 15, 15, 3, 315, 3, 15, 45, 729, 15, 105, 3, 45, 15, 105, 3, 675, 3, 15, 45, 45, 15, 105, 3, 405, 81

Offset

1,2

Links

Table of n, a(n) for n=1..81.

Formula

a(n) = A003961(A046523(n)).

Maple

a:= n-> (l-> mul(ithprime(i+1)^l[i][2], i=1..nops(l)))
        (sort(ifactors(n)[2], (x, y)->x[2]>y[2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 12 2023

Prog

(PARI) a(n) = { my(f=vecsort(factor(n)[, 2], , 4)); prod(i=1, #f, prime(i+1)^f[i]) } \\ Andrew Howroyd, Jan 12 2023
(Python)
from math import prod
from sympy import prime, factorint
def A359600(n): return prod(prime(i)**e for i, e in enumerate(sorted(factorint(n).values(), reverse=True), 2)) # Chai Wah Wu, Jan 12 2023

Crossrefs

Cf. A003961, A046523, A101296.

Cf. also A278223.

Sequence in context: A217883 A036553 A339318 * A166466 A068219 A337461

Adjacent sequences: A359597 A359598 A359599 * A359601 A359602 A359603

Keyword

nonn

Author

Antti Karttunen, Jan 12 2023

Status

approved