cp's OEIS Frontend

A259023 Numbers n such that Product_{d|n} d = k^2 for some k > n and simultaneously number k^2 + 1 is a divisorial prime (A258455).

%I A259023 #12 Apr 10 2025 23:23:10
%S A259023 24,54,56,88,154,174,238,248,266,296,328,374,378,430,442,472,488,494,
%T A259023 498,510,568,582,584,680,710,730,742,786,856,874,894,918,962,986,1038,
%U A259023 1246,1270,1406,1434,1442,1446,1542,1558,1586,1598
%N A259023 Numbers n such that Product_{d|n} d  = k^2 for some k > n and simultaneously number k^2 + 1 is a divisorial prime (A258455).
%C A259023 Product_{d|n} d is the product of divisors of n (A007955).
%C A259023 If 1+ Product_{d|k} d for k > 2 is a prime p, then p-1 is a square.
%C A259023 With number 2 complement of A259021 with respect to A118369.
%C A259023 See A258897 - divisorial primes of the form 1 + Product_{d|a(n)} d.
%H A259023 Charles R Greathouse IV, <a href="/A259023/b259023.txt">Table of n, a(n) for n = 1..10000</a>
%e A259023 The number 24 is in sequence because A007955(24) = 331776 = 576^2 and simultaneously 331777 is prime.
%o A259023 (Magma) [n: n in [1..2000] | &*(Divisors(n)) ne n^2 and IsSquare(&*(Divisors(n))) and IsPrime(&*(Divisors(n))+1)];
%o A259023 (PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
%o A259023 is(n)=my(t=A007955(n)); t>n^2 && issquare(t) && isprime(t+1) \\ _Charles R Greathouse IV_, Sep 01 2015
%Y A259023 Subsequence of A048943 (product of divisors of n is a square) and A118369 (numbers n such that Prod_{d|n} d + 1 is prime).
%Y A259023 Cf. A007955, A258455, A259020, A259021, A258897.
%K A259023 nonn
%O A259023 1,1
%A A259023 _Jaroslav Krizek_, Sep 01 2015