Voozh

A278165

Least number with the prime signature of the n-th Jacobsthal number.

1, 1, 2, 2, 2, 6, 2, 6, 12, 6, 2, 210, 2, 6, 30, 30, 2, 420, 2, 420, 30, 30, 2, 30030, 30, 6, 120, 2310, 6, 30030, 2, 210, 210, 6, 210, 19399380, 6, 6, 30, 60060, 6, 60060, 2, 30030, 4620, 30, 6, 223092870, 6, 30030, 2310, 30030, 6, 120120, 420, 510510, 210, 2310, 30, 401120980260, 2, 6, 4620, 30030, 2310, 9699690, 6, 30030, 210, 9699690, 6, 14841476269620, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Antti Karttunen (terms 1..257) & Hans Havermann, Table of n, a(n) for n = 1..1032

FORMULA

a(n) = A046523(A001045(n)).

MATHEMATICA

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@# == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ (2^n - (-1)^n)/3], {n, 120}] (* Michael De Vlieger, Nov 21 2016 *)

PROG

(PARI)

A001045(n) = (2^n - (-1)^n) / 3;

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

A278165(n) = A046523(A001045(n));

for(n=1, 257, write("b278165.txt", n, " ", A278165(n)));

(Scheme) (define (A278165 n) (A046523 (A001045 n)))

CROSSREFS

Cf. A001045, A046523.

Cf. A107036 (positions of 2's), A286565 (rgs-version of this sequence).

Cf. also A278245, A278248, A278258, A286567.

Sequence in context: A291439 A023957 A224964 * A074928 A285713 A278230