A164320 Primes p such that sums of divisors of the two adjacent integers are each > 2*p.

19, 31, 41, 71, 79, 89, 101, 103, 113, 127, 139, 197, 199, 223, 271, 281, 307, 349, 353, 367, 379, 401, 439, 449, 461, 463, 491, 499, 521, 571, 607, 617, 619, 641, 643, 701, 727, 739, 761, 769, 811, 821, 859, 881, 911, 919, 929, 941, 953, 967, 991, 1039, 1061

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

Intersection of A164318 and A164319.

Example

For p=19, the sum of the divisors of 18 is A000203(18)=39 > 2*19, and the sum of the divisors
of 20 is A000203(20)= 42 > 2*19, so p=19 is in the sequence.

Mathematica

f[n_]:=Plus@@Divisors[n]; lst={}; Do[p=Prime[n]; If[f[p-1]>2*p&&f[p+1]> 2*p, AppendTo[lst, p]], {n, 6!}]; lst
Select[Prime[Range[200]], DivisorSigma[1, #-1]>2#&&DivisorSigma[ 1, #+1]>2#&] (* Harvey P. Dale, Nov 10 2011 *)

Crossrefs

Cf. A164318, A164319.

Sequence in context: A040088 A178251 A335418 * A154418 A120337 A120115

Adjacent sequences: A164317 A164318 A164319 * A164321 A164322 A164323

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 12 2009

Extensions

References to unrelated sequences removed by R. J. Mathar, Aug 21 2009

Status

approved