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A087893 Number of numbers m satisfying 1 < m < n such that m^2 == m (mod n). 3

%I #18 May 24 2024 03:28:47

%S 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,

%T 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,

%U 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

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

%C The number of nontrivial unitary divisors of n (i.e., excluding 1 and n). - _Amiram Eldar_, May 29 2020

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

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

%H G. C. Greubel, <a href="/A087893/b087893.txt">Table of n, a(n) for n = 1..5000</a>

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

%t 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 *)

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

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

%K nonn

%O 1,6

%A _Lekraj Beedassy_, Oct 13 2003

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Last modified August 29 21:13 EDT 2024. Contains 375518 sequences. (Running on oeis4.)