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
Keywords
Examples
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.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
Programs
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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 *)
Extensions
References to unrelated sequences removed by R. J. Mathar, Aug 21 2009