A278252 Least number with the prime signature of the n-th tetrahedral number, binomial(n+2,3).

1, 4, 6, 12, 6, 24, 60, 120, 30, 60, 30, 60, 30, 240, 120, 240, 30, 420, 210, 420, 30, 120, 180, 360, 180, 1260, 420, 420, 30, 480, 240, 480, 210, 4620, 2310, 420, 30, 840, 420, 840, 30, 420, 2310, 4620, 210, 240, 360, 3600, 180, 1260, 210, 1260, 420, 27720, 4620, 840, 30, 420, 210, 420, 210, 6720, 36960, 6720, 210, 420, 210, 4620, 210, 9240, 420, 840, 60, 1260

Offset: 1

Author

Antti Karttunen, Nov 19 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Diagonal 3 of A278218.

Cf. A000292, A046523.

Programs

Mathematica

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ Binomial[n + 2, 3]], {n, 74}] (* Michael De Vlieger, Nov 21 2016 *)

PARI

a(n)=my(e=vecsort(factor(binomial(n+2,3))[,2],,4)~); factorback(primes(#e),e) \\ Charles R Greathouse IV, Feb 22 2017

Scheme

(define (A278252 n) (A046523 (A000292 n)))
(define (A000292 n) (/ (* n (+ 1 n) (+ 2 n)) 6))

Formula

a(n) = A046523(A000292(n)) = A046523(binomial(n+2,3)).