A180641 Primes P such that P > (largest prime factor of (P-1)) * (largest prime factor of (P+1)).
7, 17, 19, 31, 41, 53, 71, 79, 89, 97, 101, 109, 127, 151, 163, 181, 191, 197, 199, 239, 241, 251, 257, 271, 307, 337, 349, 379, 401, 419, 431, 433, 449, 461, 463, 487, 491, 499, 521, 571, 577, 593, 599, 601, 631, 641, 647, 659, 683, 701, 727, 751, 769, 809
Offset: 1
Keywords
Examples
Example: For n = 3, a(3)=19. The prime P = 19 P-1 = 18 (largest prime factor of 18 is 3) P+1 = 20 (largest prime factor of 20 is 5) 19 > 3*5.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
lpfQ[n_]:=Module[{a=FactorInteger[n-1][[-1,1]],b=FactorInteger[n+1][[-1,1]]},n>a*b]; Select[Prime[Range[200]],lpfQ] (* Harvey P. Dale, Aug 16 2013 *) -
PARI
lpf(n) = {f = factor(n); return (f[#f~, 1]);} lista(nn) = {forprime(p=3, nn,if ((p > lpf(p-1)*lpf(p+1)), print1(p, ", ");););} \\ Michel Marcus, Jul 25 2013