A087893 Number of numbers m satisfying 1 < m < n such that m^2 == m (mod n).

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 6, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 6, 0, 2, 2, 0, 2, 6, 0, 2, 2, 6, 0, 2, 0, 2, 2, 2, 2, 6, 0, 2, 0, 2, 0, 6, 2, 2, 2, 2, 0, 6, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 6, 0, 2, 6

Offset: 1

Author

Lekraj Beedassy, Oct 13 2003

Keywords

• nonn

Comments

The number of nontrivial unitary divisors of n (i.e., excluding 1 and n). - Amiram Eldar, May 29 2020

a(n) first deviates from b(n) = 2*A079275(n) at a(210) = 14 <> b(210) = 12. - Georg Fischer, May 23 2024

References

• C. R. J. Singleton, "Prime Function Problem": Solution to Problem 2355, Journal of Recreational Mathematics, Vol. 29(3) pp. 232-234, 1998.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001221, A007875, A034444, A079275, A309307.

Programs

Mathematica

Join[{0}, Table[2^(PrimeNu[n]) - 2, {n, 2, 50}]] (* or *) Table[2*Module[{c = PrimeNu[n]}, (c (c - 1))/2], {n, 1, 20}] (* G. C. Greubel, May 20 2017 *)

PARI

concat([0], for(n=2, 50, print1( 2^(omega(n)) - 2, ", "))) \\ G. C. Greubel, May 20 2017

Formula

a(n) = 2^omega(n) - 2 (for n > 1).