A330879 - OEIS

%I #24 Feb 01 2021 18:31:20

%S 1,4,9,12,16,25,30,36,49,56,63,64,70,72,80,81,90,100,121,132,144,169,

%T 182,195,196,208,210,224,225,240,256,289,306,324,361,380,399,400,418,

%U 420,440,441,462,484,529,552,575,576,598,600,621,624,625,644,648,650,672

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

%C For n > 0, A000290(n) is a term. - _Ivan N. Ianakiev_, May 03 2020

%C For nonsquares, d is the tau(n)/2-th divisor of n. - _David A. Corneth_, May 03 2020

%H David A. Corneth, <a href="/A330879/b330879.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 is in the sequence since it has the divisor pair (3,3) with each divisor sharing the same next prime, which is 5.

%e 12 is in the sequence since it has the divisor pair (3,4) and both 3 and 4 have 5 as their next prime.

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

%o (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

%Y Cf. A056737, A151800.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Apr 30 2020