A283759 Numbers whose Euler totient function is equal to the product of the number of divisors of their k first powers, for some k.

3, 7, 8, 10, 18, 24, 30, 57, 74, 344, 399, 494, 518, 629, 654, 679, 1154, 2408, 2989, 3048, 3175, 3458, 3789, 4218, 4578, 4890, 5022, 7668, 10602, 13720, 14647, 14701, 14837, 15613, 16133, 17563, 17945, 18335, 19608, 20195, 20358, 21243, 21336, 21423, 22083, 22503

Offset: 1

Author

Paolo P. Lava, Mar 16 2017

Keywords

• nonn

Comments

Values of k: {1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, ...}. - Michael De Vlieger, Mar 17 2017

Examples

			phi(629) = 576 and d(629) * d(629^2) * d(629^3) = 4 * 9 * 16= 576;
phi(14647) = 14400 and d(14647) * d(14647^2) * d(14647^3) * d(14647^4) = 4 * 9 * 16 * 25 = 14400.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A000005, A000010, A270389, A270713, A275660, A283757, A283758.

Programs

Maple

with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=1; k:=0; while a
				

Mathematica

Select[Range[2, 25000], Module[{k = 1, e = EulerPhi@ #, b}, While[Set[b, Product[DivisorSigma[0, #^j], {j, k}]] < e, k++]; If[b == e, True, False]] &] (* Michael De Vlieger, Mar 17 2017 *)