login
A333787
Fully multiplicative with a(2) = 2 and a(p) = p-1 for odd primes p.
3
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
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. also A329697.
Sequence in context: A206224 A035114 A202103 * A062570 A108514 A317419
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Apr 07 2020
STATUS
approved