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A181904 a(n) = 2*(4^n - 1) / A027760(n) 1
3, 5, 63, 17, 1023, 195, 16383, 4369, 262143, 31775, 4194303, 12291, 67108863, 89478485, 1073741823, 16843009, 17179869183, 172229265, 274877906943, 6663706835, 4398046511103, 254959218035, 70368744177663, 206208774147, 1125899906842623, 1501199875790165 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Clausen numbers A027760 divide 2*(4^n - 1).

LINKS

Table of n, a(n) for n=1..26.

Thomas Clausen, Lehrsatz aus einer Abhandlung ueber die Bernoulli'schen Zahlen, Astr. Nachr. 17 (1840), 351-352.

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, Vol. 7 (1877), 157-187.

MATHEMATICA

a[n_] := 2*(4^n-1)/Times @@ Select[Divisors[n]+1, PrimeQ]; Table[a[n], {n, 1, 26}] (* Jean-François Alcover, Jul 29 2013 *)

PROG

(Sage)

def A181904(n) :

    def A027760(n) :

        S = divisors(n)

        S = map(lambda i: i+1, S)

        S = filter(lambda i: is_prime(i), S)

        return mul(i for i in S)

    return 2*(4^n-1) / A027760(n)

[A181904(n) for n in (1..26)]

CROSSREFS

Cf. A002446, A027760

Sequence in context: A320082 A273254 A222644 * A319584 A318546 A076513

Adjacent sequences:  A181901 A181902 A181903 * A181905 A181906 A181907

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 01 2012

STATUS

approved

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Last modified June 28 16:56 EDT 2022. Contains 354907 sequences. (Running on oeis4.)