A278240 Least number with the prime signature of 2^n - 1.

1, 2, 2, 6, 2, 12, 2, 30, 6, 30, 6, 420, 2, 30, 30, 210, 2, 840, 2, 4620, 60, 210, 6, 60060, 30, 30, 30, 30030, 30, 60060, 2, 2310, 210, 30, 210, 38798760, 6, 30, 210, 1021020, 6, 180180, 30, 510510, 30030, 210, 30, 446185740, 6, 510510, 2310, 510510, 30, 240240, 30030, 9699690, 210, 30030, 6, 1203362940780, 2, 30, 60060, 510510, 30, 19399380, 6, 510510, 210

Offset: 1

Author

Antti Karttunen, Nov 19 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..256

Crossrefs

Cf. A000225, A046523.

Cf. A000043 (positions of 2's), A085724 (of 6's).

Cf. also A278242.

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, 69}] (* Michael De Vlieger, Nov 21 2016 *)

PARI

allocatemem(2^30);
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
A278240(n) = A046523((2^n)-1);
for(n=1, 256, write("b278240.txt", n, " ", A278240(n)));

Scheme

(define (A278240 n) (A046523 (A000225 n)))

Formula

a(n) = A046523(A000225(n)).