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

Offset: 1

Author

Antti Karttunen, Nov 19 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. A001045, A046523.

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

Cf. also A278245, A278248, A278258, A286567.

Programs

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 *)

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)))

Formula

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