A340193 a(n) = n - (Sum_{d|n} A063994(d)).

0, 0, 0, 1, 0, 1, 0, 4, 4, 3, 0, 5, 0, 5, 4, 11, 0, 10, 0, 11, 8, 9, 0, 15, 16, 11, 20, 15, 0, 15, 0, 26, 16, 15, 20, 25, 0, 17, 20, 29, 0, 25, 0, 29, 24, 21, 0, 37, 36, 38, 28, 33, 0, 43, 36, 41, 32, 27, 0, 41, 0, 29, 44, 57, 32, 41, 0, 47, 40, 49, 0, 58, 0, 35, 56, 51, 56, 55, 0, 67, 72, 39, 0, 61, 48, 41, 52, 71, 0, 63, 36

Offset: 1

Author

Antti Karttunen, Dec 31 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Inverse Möbius transform of A318840.

Cf. A063994, A340192.

Cf. also A051953.

Programs

PARI

A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
A340193(n) = (n-sumdiv(n,d,A063994(d)));

Formula

a(n) = n - A340192(n).

a(n) = Sum_{d|n} A318840(d).