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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). 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 (list; graph; refs; listen; history; text; internal format)
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).
Sequence in context: A190524 A211569 A084586 * A301575 A294156 A108215
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 01 2015
STATUS
approved

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Last modified June 18 21:05 EDT 2024. Contains 373487 sequences. (Running on oeis4.)