A282600 a(n) = Sum_(k=1..phi(n)) floor(d_k/2) where d_k are the totatives of n.

0, 0, 1, 1, 4, 2, 9, 6, 12, 8, 25, 10, 36, 18, 28, 28, 64, 24, 81, 36, 60, 50, 121, 44, 120, 72, 117, 78, 196, 56, 225, 120, 160, 128, 204, 102, 324, 162, 228, 152, 400, 120, 441, 210, 264, 242, 529, 184, 504, 240, 400, 300, 676, 234, 540, 324, 504, 392, 841, 232

Offset: 1

Author

Michel Marcus, Feb 19 2017

Keywords

• nonn
• look

Comments

The totatives of n are the numbers k <= n with gcd(k,n) = 1.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• David Zmiaikou, Origamis and permutation groups, Thesis, 2011. See p. 65.

Crossrefs

Cf. A000010, A023896, A038566, A066840, A282601.

Programs

PARI

a(n) = sum(k=1, n, (k\2)*(gcd(n, k)==1));

Formula

If n is odd, a(n) = A023896(n)/2 - A000010(n)/4;

If n is even, a(n) = A023896(n)/2 - A000010(n)/2.