A302976 a(n) = tau(n)^n mod n^tau(n).

0, 0, 8, 17, 7, 208, 30, 0, 0, 8576, 112, 0, 80, 22864, 36199, 159681, 155, 0, 116, 40062976, 83791, 142928, 255, 26138902528, 68, 302656, 362152, 454885376, 60, 544999124224, 374, 0, 226279, 629152, 399674, 27234498115233, 76, 956704, 956539, 3361080344576

Offset: 1

Author

Jaroslav Krizek, Apr 16 2018

Keywords

• nonn

Comments

tau(n) = the number of the divisors of n (A000005).

tau(n)^n > n^tau(n) for all n > 3.

Examples

			For n = 8; a(8) = 0 because tau(8)^8 mod 8^tau(8) = 4^8 mod 8^4 = 65536 mod 4096 = 0.
		

Crossrefs

Cf. A000005, A120737, A302974, A302975.

Programs

Magma

[(NumberOfDivisors(n)^n) mod (n^NumberOfDivisors(n)): n in[1..100]];

Mathematica

PowerMod[#[[2]],#[[1]],#[[1]]^#[[2]]]&/@Table[{n,DivisorSigma[0,n]},{n,40}] (* Harvey P. Dale, Jan 08 2023 *)

Formula

a(n) = A000005(n)^n mod n^A000005(n) = A302974(n) mod A302975(n).

a(A120737(n)) = 0.