A349929 Numbers k such that A349509(k) = 3.

3, 9, 27, 30, 36, 54, 81, 84, 108, 117, 162, 243, 246, 252, 270, 324, 351, 486, 567, 597, 621, 729, 732, 738, 810, 972, 975, 1053, 1089, 1155, 1215, 1380, 1407, 1458, 1467, 1701, 1896, 2187, 2190, 2196, 2268, 2439, 2736, 2916, 2919, 3159, 3240, 3267, 3645, 3789, 3888

Offset

1,1

Comments

Terms are multiples of 3. - Chai Wah Wu, Dec 06 2021

Links

David A. Corneth, Table of n, a(n) for n = 1..2137

Kevin Ryde, C Code

Mathematica

A349509[n_]:=Denominator[Binomial[n^3+6n^2-6n+2, n^3-1]/n^3]; Select[Range[346], A349509[#] == 3 &]

Prog

(Python)
from math import comb, gcd
from itertools import count, islice
def A349929gen(): # generator of terms
    for n in count(3, 3):
        if 3*gcd(comb(n*(n*(n + 6) - 6) + 2, n**3-1), n**3) == n**3:
            yield n
A349929_list = list(islice(A349929gen(), 20)) # Chai Wah Wu, Dec 06 2021
(PARI) is(n) = {if(n%3 != 0, return(0)); my(f = factor(n)); for(i = 1, #f~, c = val(n^3 + 6*n^2 - 6*n + 2, f[i, 1]) - val(n^3 - 1, f[i, 1]) - val(6*n^2 - 6*n + 3, f[i, 1]) - 3*f[i, 2]; if(f[i, 1] == 3, if(c != -1, return(0) ) , if(c < 0, return(0) ) ) ); 1 }
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Dec 06 2021
(C) See links.

Crossrefs

Cf. A008585 (supersequence), A082529, A349509.

Sequence in context: A370871 A061948 A018644 * A111117 A018675 A061972

Adjacent sequences: A349926 A349927 A349928 * A349930 A349931 A349932

Keyword

nonn

Author

Stefano Spezia, Dec 05 2021

Extensions

a(17)-a(29) from Amiram Eldar, Dec 05 2021

a(30)-a(45) from Hugo Pfoertner, Dec 06 2021

More terms from David A. Corneth, Dec 06 2021

Status

approved