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

4, 68425, 78045, 4460155, 28268625, 114468171, 177972505, 554353635, 554821905, 555758445, 556226715, 556382805, 558099795, 558724155, 560128965, 560909415, 561377685, 562470315, 562782495, 562938585, 563406855, 564187305, 564811665, 565279935, 565592115, 566060385

Offset

1,1

Comments

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

This sequence is infinite: if p >= 7103 is prime then 78045*p is a term. Terms a(8)-a(536) are of this form.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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[#] &]

Prog

(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]);
is(n) = !issquarefree(n) && iseq(n)

Crossrefs

Cf. A005117, A013929, A071324, A370681.

Sequence in context: A276718 A102200 A257769 * A066544 A009529 A339450

Adjacent sequences: A370680 A370681 A370682 * A370684 A370685 A370686

Keyword

nonn

Author

Amiram Eldar, Feb 26 2024

Status

approved