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

1,2

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A000035, A003958, A006519, A068468.

Cf. also A329697.

Sequence in context: A206224 A035114 A202103 * A062570 A108514 A317419

Adjacent sequences: A333784 A333785 A333786 * A333788 A333789 A333790

Keyword

nonn,mult

Author

Antti Karttunen, Apr 07 2020

Status

approved