A341933 a(n) = A023896(n) mod A000203(n).

0, 1, 3, 4, 4, 6, 5, 1, 1, 2, 7, 24, 8, 18, 12, 2, 10, 15, 11, 38, 30, 2, 13, 36, 2, 30, 3, 0, 16, 48, 17, 4, 42, 2, 36, 34, 20, 42, 20, 50, 22, 60, 23, 20, 72, 2, 25, 12, 3, 35, 24, 36, 28, 6, 20, 72, 66, 2, 31, 144, 32, 66, 94, 8, 48, 84, 35, 80, 78, 120, 37, 84, 38, 78, 12, 108, 6, 96, 41, 164

Offset

1,3

Comments

a(k) is the sum of totatives of k modulo the sum of divisors of k.

If p is an odd prime, a(p) = (p+3)/2 and a(p^2) = (p-1)/2.

If p is a prime == 5 (mod 6), a(2*p) = 2.

If p is a prime == 1 (mod 6), a(2*p) = 2*p+4.

Are 2, 8 and 9 the only solutions to a(k) = 1?

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(6) = 6 because the sum of totatives of 6 is 1+5 = 6, the sum of divisors of 6 is 1+2+3+6 = 12, and 6 mod 12 = 6.

Maple

f:= n -> n*numtheory:-phi(n)/2 mod numtheory:-sigma(n):
map(f, [$1..100]);

Mathematica

Array[Mod[# EulerPhi[#]/2 + Boole[# == 1]/2, DivisorSigma[1, #]] &, 80] (* Michael De Vlieger, Feb 23 2021 *)

Crossrefs

Cf. A000203, A023896, A239205, A308169.

Sequence in context: A336094 A182487 A309530 * A061117 A255171 A323712

Adjacent sequences: A341930 A341931 A341932 * A341934 A341935 A341936

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 23 2021

Status

approved