A329880 Numbers k such that the sums of unitary and nonunitary divisors of k have the same set of prime divisors.

24, 40, 56, 76, 88, 104, 108, 116, 120, 136, 152, 168, 184, 228, 232, 236, 248, 261, 264, 280, 296, 312, 316, 328, 342, 344, 348, 356, 376, 380, 408, 424, 436, 440, 456, 472, 488, 520, 522, 531, 532, 536, 540, 552, 556, 568, 580, 584, 596, 616, 632, 664, 680

Offset

1,1

Comments

Numbers k such that rad(usigma(k)) = rad(nusigma(k)), where rad(k) is the squarefree kernel of k (A007947), usigma(k) is the sum of unitary divisors of k (A034448) and nusigma(k) = sigma(k) - usigma(k) is the sum of nonunitary divisors of k (A048146).

Numbers k such that rad(usigma(k)) = rad(nusigma(k)) = rad(k) are 24, 3780, 26460, ... with no other term below 3*10^9.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger@ n); usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; Select[Range[700], rad[usigma[#]] == rad[nusigma[#]] &]

Crossrefs

Cf. A007947, A034448, A048146, A329858, A329879.

Sequence in context: A297401 A065127 A065036 * A303359 A340747 A340746

Adjacent sequences: A329877 A329878 A329879 * A329881 A329882 A329883

Keyword

nonn

Author

Amiram Eldar, Nov 23 2019

Status

approved