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

1,1

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

Links

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

Example

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.

Maple

with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do a:=1; k:=0; while a<phi(n) do k:=k+1; a:=a*tau(n^k); if phi(n)=a then print(n); break; fi; od; od; end: P(10^5);

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 *)

Crossrefs

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

Sequence in context: A050010 A316493 A213650 * A261415 A331547 A285164

Adjacent sequences: A283756 A283757 A283758 * A283760 A283761 A283762

Keyword

nonn

Author

Paolo P. Lava, Mar 16 2017

Status

approved