A278253 Least number with the prime signature of the n-th triangular number.

1, 2, 6, 6, 6, 6, 12, 36, 12, 6, 30, 30, 6, 30, 120, 24, 12, 12, 30, 210, 30, 6, 60, 180, 12, 24, 120, 30, 30, 30, 48, 240, 30, 30, 420, 60, 6, 30, 420, 60, 30, 30, 30, 420, 60, 6, 120, 360, 36, 60, 210, 30, 24, 120, 420, 420, 30, 6, 210, 210, 6, 60, 1440, 480, 210, 30, 30, 210, 210, 30, 180, 180, 6, 60, 420, 210, 210, 30, 120, 2160, 48, 6, 210, 2310, 30, 30

Offset

1,2

Links

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

Formula

a(n) = A046523(A000217(n)).

Mathematica

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ (n^2 - n)/2], {n, 2, 87}] (* Michael De Vlieger, Nov 21 2016 *)

Prog

(Scheme) (define (A278253 n) (A046523 (A000217 n)))
(PARI) a(n)=my(f=vecsort(factor(n*(n+1)/2)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ Charles R Greathouse IV, Feb 03 2017

Crossrefs

Cf. A000217, A046523, A278254, A278256.

Diagonal 2 of triangle A278218.

Sequence in context: A304363 A247097 A258576 * A294961 A048765 A103643

Adjacent sequences: A278250 A278251 A278252 * A278254 A278255 A278256

Keyword

nonn

Author

Antti Karttunen, Nov 19 2016

Status

approved