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

1,3

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

Adjacent sequences: A278162 A278163 A278164 * A278166 A278167 A278168

Keyword

nonn

Author

Antti Karttunen, Nov 19 2016

Status

approved