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Numbers k such that k and nusigma(k) have the same set of prime divisors, where nusigma(k) is the sum of nonunitary divisors of k (A048146).
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%I #9 Sep 12 2020 03:21:10

%S 4,9,24,25,49,54,112,121,150,169,289,294,361,480,529,726,750,841,961,

%T 1014,1369,1681,1734,1849,1984,2058,2166,2209,2430,2520,2688,2809,

%U 3174,3481,3721,3780,4489,5041,5046,5329,5760,5766,6241,6889,7921,7986,8214,8700

%N Numbers k such that k and nusigma(k) have the same set of prime divisors, where nusigma(k) is the sum of nonunitary divisors of k (A048146).

%C Numbers k such that rad(nusigma(k)) = rad(k), where rad(k) is the squarefree kernel of k (A007947).

%H Amiram Eldar, <a href="/A329879/b329879.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[10^4], rad[nusigma[#]] == rad[#] &]

%Y Cf. A007947, A027598, A048146, A329858.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 23 2019