A283757 Numbers n such that phi(n) = Sum_{j=1..k} d(n^j) for some k, where phi(n) is the Euler totient function of n and d(n) is the number of divisors of n.

1, 3, 8, 10, 18, 24, 30, 435, 485, 579, 678, 759, 1052, 1593, 3243, 3857, 3913, 4085, 4445, 4773, 4953, 5685, 6078, 6278, 6322, 6836, 7570, 9823, 10199, 10703, 12474, 12913, 12927, 14180, 14511, 14623, 16958, 17013, 17014, 17174, 17518, 17966, 18238, 19334, 19432

Offset

1,2

Comments

Values of k: {1, 1, 1, 1, 1, 1, 1, 4, 9, 9, 4, 5, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 16, 9, 12, 12, 12, 4, 32, 12, 9, 12, 32, 12, 13, 12, 12, 12, 12, 12, 12, 9, ...}. - Michael De Vlieger, Mar 17 2017

Links

Table of n, a(n) for n=1..45.

Example

d(1052) + d(1052^2) + d(1052^3) + d(1052^4) + d(1052^5) + d(1052^6) + d(1052^7) + d(1052^8) = 524 = phi(1052).

Maple

with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do a:=0; 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@ 4000, Module[{k = 1, e = EulerPhi@ #, b}, While[Set[b, Sum[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.

Sequence in context: A064435 A079541 A378089 * A353078 A131725 A346370

Adjacent sequences: A283754 A283755 A283756 * A283758 A283759 A283760

Keyword

nonn

Author

Paolo P. Lava, Mar 16 2017

Status

approved