A340193 -id:A340193 - cp's OEIS frontend

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

Antti Karttunen, Dec 31 2020

nonn

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

Inverse Möbius transform of A063994.

Cf. A340190, A340193.

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

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

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

A340196 a(n) = n - A340195(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 4, 4, 3, 0, 5, 0, 5, 6, 11, 0, 10, 0, 11, 8, 9, 0, 15, 16, 11, 20, 15, 0, 17, 0, 26, 16, 15, 22, 25, 0, 17, 22, 29, 0, 25, 0, 29, 30, 21, 0, 37, 36, 38, 30, 33, 0, 43, 38, 41, 32, 27, 0, 43, 0, 29, 46, 57, 32, 41, 0, 47, 40, 51, 0, 58, 0, 35, 60, 51, 56, 57, 0, 67, 72, 39, 0, 61, 60, 41, 54, 71, 0, 69

Offset: 1

Antti Karttunen, Jan 02 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Inverse Möbius transform of A318830.
Cf. A000010, A049559, A340195.
Cf. also A340193.

A049559(n) = gcd(eulerphi(n), n-1);
A318830(n) = (eulerphi(n)-A049559(n));
A340196(n) = sumdiv(n,d,A318830(d));

a(n) = Sum_{d|n} A318830(d).

cp's OEIS Frontend

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

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