A056100 a(n) = sigma(n)*phi(n) + 1 (mod n).

0, 0, 0, 3, 0, 1, 0, 5, 7, 3, 0, 5, 0, 5, 13, 9, 0, 1, 0, 17, 7, 9, 0, 1, 21, 11, 19, 1, 0, 7, 0, 17, 4, 15, 33, 13, 0, 17, 19, 1, 0, 19, 0, 9, 28, 21, 0, 17, 43, 11, 10, 13, 0, 1, 21, 25, 31, 27, 0, 49, 0, 29, 28, 33, 3, 43, 0, 21, 16, 27, 0, 1, 0, 35, 11, 25, 63, 55, 0, 33, 55, 39, 0, 1

Offset: 1

Author

Robert G. Wilson v, Jul 28 2000

Keywords

• easy
• nonn

Comments

Note that iff p is a prime then sigma(p)*phi(p) + 1 = 0 (mod p).

References

• George E. Andrews, "Number Theory," Dover Publ., NY, 1971, page 85.

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A062354.

Programs

Mathematica

Table[Mod[DivisorSigma[1, n]*EulerPhi[n] + 1, n], {n, 1, 100}]

PARI

a(n) = (sigma(n)*eulerphi(n)+1) % n; \\ Michel Marcus, Aug 05 2025

Python

from sympy import totient, divisor_sigma
def A056100(n): return (totient(n)*divisor_sigma(n)+1)%n # Karl-Heinz Hofmann, Aug 12 2025