A338224 Multiplicative with a(A246655(k)) = prime(k) for any k > 0 (where prime(k) denotes the k-th prime number).

1, 2, 3, 5, 7, 6, 11, 13, 17, 14, 19, 15, 23, 22, 21, 29, 31, 34, 37, 35, 33, 38, 41, 39, 43, 46, 47, 55, 53, 42, 59, 61, 57, 62, 77, 85, 67, 74, 69, 91, 71, 66, 73, 95, 119, 82, 79, 87, 83, 86, 93, 115, 89, 94, 133, 143, 111, 106, 97, 105, 101, 118, 187, 103

Offset: 1

Author

Rémy Sigrist, Jan 30 2021

Keywords

• nonn
• mult

Comments

All terms are distinct and squarefree.

This sequence has similarities with A160102, however some squarefree numbers do not appear here.

Examples

			a(3) = a(A246655(2)) = prime(2) = 3.
a(4) = a(A246655(3)) = prime(3) = 5.
a(12) = a(3) * a(4) = 3*5 = 15.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A160102, A246655.

Programs

PARI

pk = select(v -> omega(v)==1, [1..m=64]); for (n=1, m, f=factor(n); print1 (prod(k=1, #f~, prime(setsearch(pk, f[k,1]^f[k,2])))", "))

Python

from math import prod
from sympy import prime, primepi, integer_nthroot, factorint
def A338224(n): return prod(prime(sum(primepi(integer_nthroot(p**e,k)[0]) for k in range(1,(p**e).bit_length()))) for p, e in factorint(n).items()) # Chai Wah Wu, Jan 19 2025