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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). 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

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