A278258 Least number with the prime signature of the n-th Catalan number.

1, 1, 2, 2, 6, 30, 60, 30, 210, 210, 420, 2310, 4620, 13860, 360360, 60060, 1021020, 9699690, 58198140, 223092870, 446185740, 446185740, 892371480, 1338557220, 1338557220, 6692786100, 2677114440, 12939386460, 802241960520, 802241960520, 1604483921040, 200560490130, 14841476269620, 608500527054420, 608500527054420, 304250263527210, 608500527054420, 608500527054420

Offset: 0

Author

Antti Karttunen, Nov 19 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A000108, A046523.

Cf. also A278241, A278245, A278248, A278250, A278165.

Programs

Mathematica

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[CatalanNumber@ n], {n, 0, 37}] (* Michael De Vlieger, Nov 21 2016 *)

PARI

A000108(n) = binomial(2*n, n)/(n+1);
A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ From Charles R Greathouse IV, Aug 17 2011
A278258(n) = A046523(A000108(n));
for(n=0, 150, write("b278258.txt", n, " ", A278258(n)));

Scheme

(define (A278258 n) (A046523 (A000108 n)))

Formula

a(n) = A046523(A000108(n)).