A358929 a(n) is the smallest centered triangular number with exactly n prime factors (counted with multiplicity).

1, 19, 4, 316, 136, 760, 64, 4960, 22144, 103360, 27136, 5492224, 1186816, 41414656, 271212544, 559980544, 1334788096, 12943360, 7032930304, 527049293824, 158186536960, 1096295120896, 7871801589760, 154690378792960, 13071965224960, 56262393856, 964655941943296

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Centered Triangular Number

Eric Weisstein's World of Mathematics, Prime Factor

Example

a(4) = 136, because 136 is a centered triangular number with 4 prime factors (counted with multiplicity) {2, 2, 2, 17} and this is the smallest such number.

Mathematica

c[k_] := (3*k^2 + 3*k + 2)/2; a[n_] := Module[{k = 0, ck}, While[PrimeOmega[ck = c[k]] != n, k++]; ck]; Array[a, 18, 0] (* Amiram Eldar, Dec 09 2022 *)

Prog

(PARI) a(n) = if(n==0, return(1)); for(k=1, oo, my(t=3*k*(k+1)/2 + 1); if(bigomega(t) == n, return(t))); \\ Daniel Suteu, Dec 10 2022

Crossrefs

Cf. A001222, A005448, A075088, A358926, A358927, A358928.

Sequence in context: A274249 A040350 A089572 * A040348 A128050 A365815

Adjacent sequences: A358926 A358927 A358928 * A358930 A358931 A358932

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 06 2022

Extensions

a(22)-a(26) from Daniel Suteu, Dec 10 2022

Status

approved