A079151 Primes p such that p-1 has at most 3 prime factors, counted with multiplicity; i.e., primes p such that bigomega(p-1) = A001222(p-1) <= 3.
2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 43, 47, 53, 59, 67, 71, 79, 83, 103, 107, 131, 139, 149, 167, 173, 179, 191, 223, 227, 239, 263, 269, 283, 293, 311, 317, 347, 359, 367, 383, 389, 419, 431, 439, 443, 467, 479, 499, 503, 509, 557, 563, 587, 599, 607, 619, 643
Offset: 1
Examples
149 is in the sequence because 149 - 1 = 2*2*37 has 3 prime factors.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
s[n_] := Reap[sr = 0; ct = 0; For[x = 2, x <= n, x = NextPrime[x], If[PrimeOmega[x - 1] < 4, Sow[x]; sr += 1.0/x; ct += 1]]][[2, 1]]; s[700] (* Jean-François Alcover, Jun 08 2013, translated and adapted from Pari *) Select[Prime[Range[120]],PrimeOmega[#-1]<4&] (* Harvey P. Dale, Oct 02 2017 *)
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PARI
s(n)=sr=0; ct=0; forprime(x=2,n, if(bigomega(x-1) < 4, print1(x" "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); \\ Lists primes p<=n such that p-1 has at most 3 prime factors.
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PARI
list(lim)=my(v=List([2,3]),t); forprime(p=2,(lim-1)\2, if(isprime(t=2*p+1), listput(v,t))); forprime(p=2,(lim-1)\4, forprime(q=2,min(p,(lim-1)\2\p), if(isprime(t=2*p*q+1), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Mar 06 2017
Extensions
Typos in definition corrected by Harvey P. Dale, Oct 02 2017
Comments