A329879 -id:A329879 - cp's OEIS frontend

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

Amiram Eldar, Nov 23 2019

nonn

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.

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

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

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[#]] &]

cp's OEIS Frontend

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

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