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

Author

Antti Karttunen, Jan 12 2023

Keywords

• nonn

Crossrefs

Cf. A003961, A046523, A101296.

Cf. also A278223.

Programs

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

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

Formula

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