cp's OEIS Frontend

A358816 Numbers k such that d + k/d is prime for any unitary divisor d of k.

%I A358816 #8 Feb 16 2025 08:34:04
%S A358816 1,2,4,6,10,12,16,18,22,28,30,36,40,42,52,58,60,70,72,78,82,88,100,
%T A358816 102,108,112,130,148,162,172,190,192,196,198,210,228,232,240,250,256,
%U A358816 268,270,280,310,312,316,330,352,358,372,378,382,388,396,400,408,432,442,448
%N A358816 Numbers k such that d + k/d is prime for any unitary divisor d of k.
%C A358816 A unitary divisor d of k is a number d such that d|k and gcd(d, k/d) = 1.
%C A358816 A080715 is the subsequence of the squarefree terms of this sequence.
%H A358816 Amiram Eldar, <a href="/A358816/b358816.txt">Table of n, a(n) for n = 1..10000</a>
%H A358816 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnitaryDivisor.html">Unitary Divisor</a>.
%H A358816 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unitary_divisor">Unitary divisor</a>.
%t A358816 q[n_] := AllTrue[Select[Divisors[n], #^2 < n && CoprimeQ[#, n/#] &], PrimeQ[# + n/#] &]; Select[Prime[Range[90]] - 1, q]
%o A358816 (PARI) is(n) = fordiv(n, d, if(d < n^2 && gcd(d, n/d) == 1 && !isprime(d+n/d), return(0))); return(1);
%Y A358816 Cf. A005117, A077610, A080715.
%Y A358816 Subsequence of A006093.
%K A358816 nonn
%O A358816 1,2
%A A358816 _Amiram Eldar_, Dec 02 2022