OFFSET
1,4
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Andrew V. Lelechenko, Exponential and infinitary divisors, Ukrainian Mathematical Journal, Vol. 68, No. 8 (2017), pp. 1222-1237; arXiv preprint, arXiv:1405.7597 [math.NT] (2014).
FORMULA
Multiplicative with a(p^e) = A037445(e).
Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = Product_{p prime} (1 + Sum_{k>=2} (d(k) - d(k-1))/p^k) = 1.5482125828..., where d(k) = A037445(k). - Amiram Eldar, Nov 08 2020
MATHEMATICA
di[1] = 1; di[n_] := Times @@ Flatten[ 2^DigitCount[#, 2, 1]& /@ FactorInteger[n][[All, 2]] ]; fun[p_, e_] := di[e]; a[1] = 1; a[n_] := Times @@ (fun @@@ FactorInteger[n]); Array[a, 100] (* after Jean-François Alcover at A037445 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, May 01 2019
STATUS
approved