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

0,3

Links

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

Formula

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

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 *)

Prog

(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)))

Crossrefs

Cf. A000108, A046523.

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

Sequence in context: A270487 A058250 A179929 * A067644 A184312 A097801

Adjacent sequences: A278255 A278256 A278257 * A278259 A278260 A278261

Keyword

nonn

Author

Antti Karttunen, Nov 19 2016

Status

approved