cp's OEIS Frontend

A344875 Multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e - 1 for odd primes p.

%I A344875 #32 Jan 21 2025 18:18:54
%S A344875 1,3,2,7,4,6,6,15,8,12,10,14,12,18,8,31,16,24,18,28,12,30,22,30,24,36,
%T A344875 26,42,28,24,30,63,20,48,24,56,36,54,24,60,40,36,42,70,32,66,46,62,48,
%U A344875 72,32,84,52,78,40,90,36,84,58,56,60,90,48,127,48,60,66,112,44,72,70,120,72,108,48,126,60,72,78,124,80,120
%N A344875 Multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e - 1 for odd primes p.
%H A344875 Antti Karttunen, <a href="/A344875/b344875.txt">Table of n, a(n) for n = 1..10000</a>
%F A344875 a(n) = A344878(n) * A344879(n).
%F A344875 Multiplicative with a(p^e) = A153151(p^e). - _Antti Karttunen_, Jul 01 2021
%F A344875 Sum_{k=1..n} a(k) ~ c * n^2, where c = (4/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (4/5) * A065463 = 0.563553... . - _Amiram Eldar_, Nov 18 2022
%t A344875 f[2, e_] := 2^(e + 1) - 1; f[p_, e_] := p^e - 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jun 03 2021 *)
%o A344875 (PARI) A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A344875 (Python)
%o A344875 from math import prod
%o A344875 from sympy import factorint
%o A344875 def A344875(n): return prod((p**(1+e) if p == 2 else p**e)-1 for p, e in factorint(n).items()) # _Chai Wah Wu_, Jun 01 2022
%Y A344875 Cf. A047994, A065463, A153151, A344876, A344877, A344878, A344879, A344969, A345947.
%K A344875 nonn,mult
%O A344875 1,2
%A A344875 _Antti Karttunen_, Jun 03 2021