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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
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
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
Sequence in context: A034018 A320924 A357976 * A357636 A363261 A360953
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 30 2020
STATUS
approved