A340192 a(n) = Sum_{d|n} A063994(d), where A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

1, 2, 3, 3, 5, 5, 7, 4, 5, 7, 11, 7, 13, 9, 11, 5, 17, 8, 19, 9, 13, 13, 23, 9, 9, 15, 7, 13, 29, 15, 31, 6, 17, 19, 15, 11, 37, 21, 19, 11, 41, 17, 43, 15, 21, 25, 47, 11, 13, 12, 23, 19, 53, 11, 19, 15, 25, 31, 59, 19, 61, 33, 19, 7, 33, 25, 67, 21, 29, 21, 71, 14, 73, 39, 19, 25, 21, 23, 79, 13, 9, 43, 83, 23, 37

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

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

Formula

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

a(n) = n - A340193(n).

Prog

(PARI)
A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
A340192(n) = sumdiv(n, d, A063994(d));

Crossrefs

Inverse Möbius transform of A063994.

Cf. A340190, A340193.

Sequence in context: A146071 A167411 A340195 * A363321 A112823 A247176

Adjacent sequences: A340189 A340190 A340191 * A340193 A340194 A340195

Keyword

nonn

Author

Antti Karttunen, Dec 31 2020

Status

approved