cp's OEIS Frontend

A095691 Multiplicative with a(p^e) = A000720(e)+1.

%I A095691 #20 Nov 02 2023 10:28:06
%S A095691 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,3,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,4,1,1,
%T A095691 1,4,1,1,1,3,1,1,1,2,2,1,1,3,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,4,1,1,1,2,
%U A095691 1,1,1,6,1,1,2,2,1,1,1,3,3,1,1,2,1,1,1,3,1,2,1,2,1,1,1,4,1,2,2,4,1,1,1,3,1
%N A095691 Multiplicative with a(p^e) = A000720(e)+1.
%C A095691 The number of divisors of n that are terms of A056166. - _Amiram Eldar_, Oct 31 2023
%H A095691 Antti Karttunen, <a href="/A095691/b095691.txt">Table of n, a(n) for n = 1..10000</a>
%H A095691 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A095691 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + Sum_{q prime} 1/p^q) = Sum_{n>=1} 1/A056166(n) = 1.80728269690724154161... . - _Amiram Eldar_, Oct 31 2023
%t A095691 Array[Times @@ Map[PrimePi@# + 1 &, FactorInteger[#][[All, -1]] ] &, 120] (* _Michael De Vlieger_, Jul 19 2017 *)
%o A095691 (PARI) A095691(n) = { my(f = factor(n), m = 1); for (k=1, #f~, m *= (1+primepi(f[k, 2])); ); m; } \\ _Antti Karttunen_, Jul 19 2017
%o A095691 (Python)
%o A095691 from sympy import factorint, primepi, prod
%o A095691 def a(n): return 1 if n==1 else prod(primepi(e) + 1 for e in factorint(n).values())
%o A095691 print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Jul 19 2017
%Y A095691 Cf. A000720, A056166, A095683.
%K A095691 mult,nonn,easy
%O A095691 1,4
%A A095691 _Vladeta Jovovic_, Jul 06 2004