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A341933
a(n) = A023896(n) mod A000203(n).
1
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 23 2021
STATUS
approved