

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
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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)/2th 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



