A333787 Fully multiplicative with a(2) = 2 and a(p) = p-1 for odd primes p.

1, 2, 2, 4, 4, 4, 6, 8, 4, 8, 10, 8, 12, 12, 8, 16, 16, 8, 18, 16, 12, 20, 22, 16, 16, 24, 8, 24, 28, 16, 30, 32, 20, 32, 24, 16, 36, 36, 24, 32, 40, 24, 42, 40, 16, 44, 46, 32, 36, 32, 32, 48, 52, 16, 40, 48, 36, 56, 58, 32, 60, 60, 24, 64, 48, 40, 66, 64, 44, 48, 70, 32, 72, 72, 32, 72, 60, 48, 78, 64, 16, 80, 82, 48, 64

Offset: 1

Author

Antti Karttunen, Apr 07 2020

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000035, A003958, A006519, A068468.

Cf. also A329697.

Programs

Mathematica

Array[If[# == 1, 1, Apply[Times, FactorInteger[#] /. {p_Integer, e_Integer} :> If[p == 2, 2, p - 1]^e]] &, 85]  (* Michael De Vlieger, Apr 15 2020 *)

PARI

A333787(n) = { my(f=factor(n)); for(i=1,#f~,f[i,1] -= (f[i,1]%2)); factorback(f); };

Formula

Multiplicative with a(p^e) = (p-A000035(p))^e.

a(n) = A003958(n) * A006519(n).

Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^4/(210*zeta(3)) = (3/4) * A068468 = 0.385882... . - Amiram Eldar, Nov 10 2022