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A362969 Nonunitary near-perfect numbers: k such that nusigma(k) = k + d where d is a nonunitary divisor of k.

%I A362969 #45 May 20 2023 04:35:51
%S A362969 48,80,96,160,224,352,416,480,896,1472,1476,1856,2688,3968,6016,7552,
%T A362969 7808,8550,8700,10332,17010,20300,22496,36448,44384,54944,63488,65024,
%U A362969 71264,73710,97300,97792,114176,122368,128512,310976,392192,490496,515072,521216,549990
%N A362969 Nonunitary near-perfect numbers: k such that nusigma(k) = k + d where d is a nonunitary divisor of k.
%C A362969 The nonunitary version of near-perfect numbers (A181595).
%H A362969 Amiram Eldar, <a href="/A362969/b362969.txt">Table of n, a(n) for n = 1..250</a>
%e A362969 For k = 352, nusigma(352) = 360. 360 - 352 = 8, which is a nonunitary divisor of 352.
%t A362969 q[n_] := Module[{d = Select[Divisors[n], ! CoprimeQ[#, n/#] &], s}, s = Total[d]; AnyTrue[d, n + # == s &]]; Select[Range[10^4], q] (* _Amiram Eldar_, May 11 2023 *)
%o A362969 (PARI) nusigma(n) = {my(f = factor(n)); sigma(f) - prod(i = 1, #f~, f[i, 1]^f[i, 2] + 1);}
%o A362969 is(n) = {my(d = nusigma(n) - n); d > 0 && !(n%d) && gcd(d, n/d) > 1; } \\ _Amiram Eldar_, May 20 2023
%Y A362969 Cf. A048146 (nusigma), A181595.
%K A362969 nonn
%O A362969 1,1
%A A362969 _Jenaro Tomaszewski_, May 10 2023