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

1,2

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: A034018 A320924 A357976 * A357636 A363261 A360953

Adjacent sequences: A330876 A330877 A330878 * A330880 A330881 A330882

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 30 2020

Status

approved