A188579 Numbers m for which max_{2<=k<(m-2)/2} Sum_{d>1: d|m-k, k|m-d} 1 = 3.

10, 15, 17, 20, 23, 25, 29, 31, 37, 40, 41, 43, 53, 67, 71, 73, 79, 89, 97, 109, 127, 151, 157, 181, 193, 239, 241, 271, 313, 331, 337, 349, 373, 397, 421, 433, 449, 601, 613, 661, 673, 701, 757, 811, 1009, 1021, 1051, 1117, 1249, 1471, 1531, 1741

Offset: 1

Author

Vladimir Shevelev, Apr 04 2011

Keywords

• nonn

Comments

All terms a(n) >= 41 are primes. - Vladimir Shevelev, May 12 2013

If prime p is in the sequence, then either (p-2,p) is a twin prime pair, or p-2 = q*r, where q and r are distinct primes, or p-2 is the cube of a prime. - Vladimir Shevelev, May 15 2013

Examples

			Let n=10. Then k takes the values 2 and 3. If k=3, then d=7 and k divides n-d; if k=2, then d = 2,4,8, n-d = 8,6,2 and k divides all these values. Since max(1,3) = 3, 10 is in the sequence. - _Vladimir Shevelev_, May 12 2013
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..215
• Vladimir Shevelev, Proof that all terms >= 41 of A188579 are primes, SeqFan Mailing List, May 15, 2013.

Crossrefs

Cf. A188550.