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

1,4

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000010, A000203, A062354.

Sequence in context: A381641 A100574 A342122 * A141665 A136689 A359364

Adjacent sequences: A056097 A056098 A056099 * A056101 A056102 A056103

Keyword

easy,nonn

Author

Robert G. Wilson v, Jul 28 2000

Status

approved