A370683 - OEIS

%I #9 Feb 27 2024 01:26:48

%S 4,68425,78045,4460155,28268625,114468171,177972505,554353635,

%T 554821905,555758445,556226715,556382805,558099795,558724155,

%U 560128965,560909415,561377685,562470315,562782495,562938585,563406855,564187305,564811665,565279935,565592115,566060385

%N Nonsquarefree numbers k such that A370681(k) = A071324(k).

%C For every squarefree number k, A370681(k) = A071324(k), since all the divisors of a squarefree number are unitary.

%C 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 Amiram Eldar, <a href="/A370683/b370683.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 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 (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 is(n) = !issquarefree(n) && iseq(n)

%Y Cf. A005117, A013929, A071324, A370681.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 26 2024