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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.
2
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 16 2017
STATUS
approved