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A370683 Nonsquarefree numbers k such that A370681(k) = A071324(k).

%I A370683 #9 Feb 27 2024 01:26:48
%S A370683 4,68425,78045,4460155,28268625,114468171,177972505,554353635,
%T A370683 554821905,555758445,556226715,556382805,558099795,558724155,
%U A370683 560128965,560909415,561377685,562470315,562782495,562938585,563406855,564187305,564811665,565279935,565592115,566060385
%N A370683 Nonsquarefree numbers k such that A370681(k) = A071324(k).
%C A370683 For every squarefree number k, A370681(k) = A071324(k), since all the divisors of a squarefree number are unitary.
%C A370683 This sequence is infinite: if p >= 7103 is prime then 78045*p is a term. Terms a(8)-a(536) are of this form.
%H A370683 Amiram Eldar, <a href="/A370683/b370683.txt">Table of n, a(n) for n = 1..10000</a>
%e A370683 4 is a term since its divisors are 1, 2 and 4, and its unitary divisors are 1 and 4, and 4 - 2 + 1 = 4 - 1.
%t A370683 q[n_] := Module[{d = Reverse[Divisors[n]], u}, u = Select[d, CoprimeQ[#, n/#] &]; Total[(-1)^(Range[Length[d]] + 1)*d] == Total[(-1)^(Range[Length[u]] + 1)*u]]; Select[Range[10^5], ! SquareFreeQ[#] && q[#] &]
%o A370683 (PARI) iseq(n) = my(d = Vecrev(divisors(n)), u = select(x->(gcd(x, n/x) == 1), d)); sum(i=1, #d, (-1)^(i+1)*d[i]) == sum(i=1, #u, (-1)^(i+1)*u[i]);
%o A370683 is(n) = !issquarefree(n) && iseq(n)
%Y A370683 Cf. A005117, A013929, A071324, A370681.
%K A370683 nonn
%O A370683 1,1
%A A370683 _Amiram Eldar_, Feb 26 2024