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 A330879 Numbers with a divisor pair (d,n/d) such that the smallest prime greater than d and n/d is the same. 1
 1, 4, 9, 12, 16, 25, 30, 36, 49, 56, 63, 64, 70, 72, 80, 81, 90, 100, 121, 132, 144, 169, 182, 195, 196, 208, 210, 224, 225, 240, 256, 289, 306, 324, 361, 380, 399, 400, 418, 420, 440, 441, 462, 484, 529, 552, 575, 576, 598, 600, 621, 624, 625, 644, 648, 650, 672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n > 0, A000290(n) is a term. - Ivan N. Ianakiev, May 03 2020 For nonsquares, d is the tau(n)/2-th divisor of n. - David A. Corneth, May 03 2020 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 EXAMPLE 9 is in the sequence since it has the divisor pair (3,3) with each divisor sharing the same next prime, which is 5. 12 is in the sequence since it has the divisor pair (3,4) and both 3 and 4 have 5 as their next prime. MATHEMATICA Table[If[Sum[KroneckerDelta[NextPrime[i], NextPrime[n/i]] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}] > 0, n, {}], {n, 500}] // Flatten PROG (PARI) isok(n) = fordiv(n, d, if (nextprime(d+1) == nextprime(n/d+1), return (1)); if (d>n/d, break)); \\ Michel Marcus, Apr 30 2020 CROSSREFS Cf. A056737, A151800. Sequence in context: A034019 A034018 A320924 * A285419 A047461 A276873 Adjacent sequences:  A330876 A330877 A330878 * A330880 A330881 A330882 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Apr 30 2020 STATUS approved

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Last modified July 26 01:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)