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

1,1

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.

Links

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

Example

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

Prog

(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

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.

Sequence in context: A190524 A211569 A084586 * A301575 A294156 A108215

Adjacent sequences: A259020 A259021 A259022 * A259024 A259025 A259026

Keyword

nonn

Author

Jaroslav Krizek, Sep 01 2015

Status

approved