OFFSET
1,3
COMMENTS
a(2n+1) is the conjectured value of the length of period of sequence of Genocchi number of first kind read modulo (2n + 1) (cf. A001469).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n*A173557(n)/2. - R. J. Mathar, Apr 14 2011
From Jianing Song, Nov 22 2018: (Start)
Multiplicative with a(p^e) = (p - 1)*p^e/2 = A000217(p-1)*p^(e-1).
a(prime(n)) = A034953(n).
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 2/(p-1)^2) = 5.72671092223951683002237367406848393189560038246828458038126468772919585... - Vaclav Kotesovec, Sep 20 2020
From Jianing Song, Aug 11 2023: (Start)
a(n) = phi(n) * Product_{p|n, p prime} (p/2), where phi = A000010.
MAPLE
A023900 := proc(n) add( d*numtheory[mobius](d), d=numtheory[divisors](n)) ; end proc:
A001221 := proc(n) nops(numtheory[factorset](n)) ; end proc:
seq(A090780(n), n=1..20) ; # R. J. Mathar, Apr 14 2011
MATHEMATICA
a[n_] := Module[{f, p, e}, fun[p_, e_] := (p - 1)*p^e/2;
If[n == 1, 1, Times @@ (fun @@@ FactorInteger[n])]]; Array[a, 50] (* Amiram Eldar, Nov 23 2018 *)
PROG
(PARI) a(n) = my(f=factor(n)[, 1]); n*prod(k=1, #f, (f[k]-1)/2); \\ Michel Marcus, May 26 2019
(PARI) a(n) = eulerphi(n)*factorback(factorint(n)[, 1]/2) \\ Jianing Song, Aug 11 2023
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Benoit Cloitre, Feb 12 2004
STATUS
approved