A358927 a(n) is the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists.

1, -1, 4, 20, 56, 120, 560, 4960, 19600, 41664, 341376, 695520, 7207200, 22238720, 178433024, 1429559296, 179481600, 11453245440, 11444858880, 393079864320, 3928874471424, 5864598896640, 46910348656640, 975649558118400, 3002365391929344, 7805131503206400

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Prime Factor

Eric Weisstein's World of Mathematics, Tetrahedral Number

Example

a(4) = 56, because 56 is a tetrahedral number with 4 prime factors (counted with multiplicity) {2, 2, 2, 7} and this is the smallest such number.

Mathematica

t[k_] := k*(k + 1)*(k + 2)/6; a[n_] := Module[{k = 1, tk}, While[PrimeOmega[tk = t[k]] != n, k++]; tk]; a[1] = -1; Array[a, 26, 0] (* Amiram Eldar, Dec 09 2022 *)

Crossrefs

Cf. A000292, A001222, A075088, A156329, A279082, A358865.

Sequence in context: A035007 A047810 A002492 * A127920 A060122 A066970

Adjacent sequences: A358924 A358925 A358926 * A358928 A358929 A358930

Keyword

sign

Author

Ilya Gutkovskiy, Dec 06 2022

Status

approved