The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A332740 Prime numbers p such that the set of composite numbers in the range [p+1, nextprime(p)-1] has more than one element and all the elements have the same number of divisors. 1
 229, 8293, 9829, 14887, 16087, 20389, 21493, 44983, 50581, 53887, 57943, 63463, 64663, 72223, 81547, 93253, 108343, 134917, 138727, 143239, 157207, 192613, 199669, 203653, 206407, 210853, 218839, 244837, 248749, 251287, 255049, 262693, 280183, 296437, 300319 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding numbers of divisors are 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 24, 24, ... and the number of divisors in the order of their first appearance are 8, 16, 24, 20, 12, 32, 48, ... The number of composites between a(n) and its next prime are 3, 3, 3, 3, 3, 3, 5, 3, 5, 3, ... Are there terms with number of composites larger than 5? LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 229 is a term since between 229 and its next prime, 233, there are 3 composite numbers, 230, 231 and 232 and all of them have the same number of divisors, 8. MATHEMATICA seqQ[n_] := PrimeQ[n] && (nx=NextPrime[n]) > n + 2 && Length @ Union @ DivisorSigma[0, Range[n+1, nx-1]] == 1; Select[Range[10^6], seqQ] CROSSREFS Cf. A000005, A075580, A075583, A075584, A075585, A075586, A075587, A075588, A075589. Sequence in context: A210514 A142665 A124684 * A178673 A028452 A072020 Adjacent sequences:  A332737 A332738 A332739 * A332741 A332742 A332743 KEYWORD nonn AUTHOR Amiram Eldar, Feb 21 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 28 14:04 EDT 2021. Contains 346334 sequences. (Running on oeis4.)