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

1,2

Comments

All terms are distinct and squarefree.

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A005117, A160102, A246655.

Sequence in context: A122637 A076229 A160102 * A355701 A353955 A318954

Adjacent sequences: A338221 A338222 A338223 * A338225 A338226 A338227

Keyword

nonn,mult

Author

Rémy Sigrist, Jan 30 2021

Status

approved