

A259023


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


4



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
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OFFSET

1,1


COMMENTS

Product_{dn} d is the product of divisors of n (A007955).
If 1+ Product_{dk} d for k > 2 is a prime p, then p1 is a square.
See A258897  divisorial primes of the form 1 + Product_{da(n)} d.


LINKS



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))


CROSSREFS

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


KEYWORD

nonn


AUTHOR



STATUS

approved



