A329897 Numbers k for which the 2-adic and 3-adic valuations of A025487(k) are equal, where A025487(k) is the k-th number which is a product of primorial numbers.

1, 4, 9, 11, 20, 22, 23, 38, 41, 43, 44, 54, 69, 72, 73, 77, 79, 93, 110, 114, 118, 123, 124, 128, 129, 131, 147, 154, 181, 186, 190, 191, 199, 201, 208, 209, 212, 232, 242, 245, 246, 272, 279, 286, 294, 299, 300, 307, 310, 312, 321, 324, 327, 345, 359, 371, 374, 376, 416, 424, 425, 430, 434, 442, 446, 451, 454, 466, 469

Offset

1,2

Comments

Numbers k for which A007814(A025487(k)) = A007949(A025487(k)).

Numbers k for which A181815(k) is odd.

Links

Antti Karttunen, Table of n, a(n) for n = 1..7806

Mathematica

s = {1}; k = 1; Do[If[GreaterEqual @@ (f = FactorInteger[n])[[;; , 2]] && PrimePi[f[[-1, 1]]] == Length[f], k++; If[Equal @@ IntegerExponent[n, {2, 3}], AppendTo[s, k]]], {n, 2, 10^5}]; s (* Amiram Eldar, Jul 28 2023 *)

Prog

(Python)
from itertools import count, islice
from heapq import heappop, heappush
from sympy import multiplicity, factorint, prevprime, nextprime
def A329897_gen(): # generator of terms
    h, hset = [1], {1}
    for c in count(1):
        m = heappop(h)
        if multiplicity(3, m)==(~m&m-1).bit_length():
            yield c
        ps = factorint(m)
        for p in ps:
            if p == 2 or ps[prevprime(p)]>ps[p]:
                mp = m*p
                if mp not in hset:
                    heappush(h, mp)
                    hset.add(mp)
        mp = m*nextprime(max(ps.keys(), default=1))
        if mp not in hset:
            heappush(h, mp)
            hset.add(mp)
A329897_list = list(islice(A329897_gen(), 69)) # Chai Wah Wu, Mar 31 2026

Crossrefs

Cf. A007814, A007949, A025487, A329898 (complement), A330682 (characteristic function).

Sequence A330683 sorted into ascending order.

Positions of odd terms in A181815.

Sequence in context: A206523 A312844 A181448 * A365892 A312845 A312846

Adjacent sequences: A329894 A329895 A329896 * A329898 A329899 A329900

Keyword

nonn

Author

Antti Karttunen, Dec 24 2019

Status

approved