A345939 a(n) = (n-1) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.

0, 1, 1, 1, 1, 5, 1, 1, 1, 9, 1, 11, 1, 13, 7, 1, 1, 17, 1, 19, 5, 21, 1, 23, 1, 25, 1, 3, 1, 29, 1, 1, 8, 33, 17, 35, 1, 37, 19, 39, 1, 41, 1, 43, 11, 45, 1, 47, 1, 49, 25, 17, 1, 53, 27, 55, 14, 57, 1, 59, 1, 61, 31, 1, 4, 13, 1, 67, 17, 23, 1, 71, 1, 73, 37, 25, 19, 77, 1, 79, 1, 81, 1, 83, 21, 85, 43, 87, 1, 89, 5, 91

Offset

1,6

Links

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

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = (n-1) / A345937(n) = (n-1) / gcd(n-1, A047994(n)).

a(2n-1) = A345949(2n-1), for n > 1.

Mathematica

uphi[1]=1; uphi[n_]:=Times@@(#[[1]]^#[[2]]-1&/@FactorInteger[n]);
a[n_]:=(n-1)/GCD[n-1, uphi[n]]; Array[a, 100] (* Giorgos Kalogeropoulos, Jul 02 2021 *)

Prog

(PARI)
A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A345939(n) = ((n-1) / gcd(n-1, A047994(n)));

Crossrefs

Cf. A047994, A345937, A345938.

Cf. also A160596, A340089, A345949.

Sequence in context: A322837 A348978 A168677 * A140210 A380400 A360720

Adjacent sequences: A345936 A345937 A345938 * A345940 A345941 A345942

Keyword

nonn

Author

Antti Karttunen, Jun 29 2021

Status

approved