A330879 Numbers with a divisor pair (d,n/d) such that the smallest prime greater than d and n/d is the same.

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

Author

Wesley Ivan Hurt, Apr 30 2020

Keywords

• nonn

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

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056737, A151800.

Programs

Mathematica

Table[If[Sum[KroneckerDelta[NextPrime[i], NextPrime[n/i]] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}] > 0, n, {}], {n, 500}] // Flatten

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