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).

24, 54, 56, 88, 154, 174, 238, 248, 266, 296, 328, 374, 378, 430, 442, 472, 488, 494, 498, 510, 568, 582, 584, 680, 710, 730, 742, 786, 856, 874, 894, 918, 962, 986, 1038, 1246, 1270, 1406, 1434, 1442, 1446, 1542, 1558, 1586, 1598

Offset: 1

Author

Jaroslav Krizek, Sep 01 2015

Keywords

• nonn

Comments

Product_{d|n} d is the product of divisors of n (A007955).

If 1+ Product_{d|k} d for k > 2 is a prime p, then p-1 is a square.

With number 2 complement of A259021 with respect to A118369.

See A258897 - divisorial primes of the form 1 + Product_{d|a(n)} d.

Examples

			The number 24 is in sequence because A007955(24) = 331776 = 576^2 and simultaneously 331777 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A048943 (product of divisors of n is a square) and A118369 (numbers n such that Prod_{d|n} d + 1 is prime).

Cf. A007955, A258455, A259020, A259021, A258897.

Programs

Magma

[n: n in [1..2000] | &*(Divisors(n)) ne n^2 and IsSquare(&*(Divisors(n))) and IsPrime(&*(Divisors(n))+1)];

PARI

A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
is(n)=my(t=A007955(n)); t>n^2 && issquare(t) && isprime(t+1) \\ Charles R Greathouse IV, Sep 01 2015