A329880 - OEIS

%I #9 Sep 12 2020 03:21:07

%S 24,40,56,76,88,104,108,116,120,136,152,168,184,228,232,236,248,261,

%T 264,280,296,312,316,328,342,344,348,356,376,380,408,424,436,440,456,

%U 472,488,520,522,531,532,536,540,552,556,568,580,584,596,616,632,664,680

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

%C 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).

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

%H Amiram Eldar, <a href="/A329880/b329880.txt">Table of n, a(n) for n = 1..10000</a>

%t 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[#]] &]

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 23 2019