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

1,6

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A294902 A321516 A172246 * A079169 A345060 A097106

Adjacent sequences: A087890 A087891 A087892 * A087894 A087895 A087896

Keyword

nonn

Author

Lekraj Beedassy, Oct 13 2003

Status

approved