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A096163 Primes p of the form qrs + 1 where q, r and s are distinct primes. 0
31, 43, 67, 71, 79, 103, 131, 139, 191, 223, 239, 283, 311, 367, 419, 431, 439, 443, 499, 599, 607, 619, 643, 647, 659, 683, 743, 787, 823, 827, 907, 947, 971, 1031, 1039, 1087, 1091, 1103, 1163, 1223, 1259, 1399, 1427, 1447, 1499, 1511, 1543, 1559, 1571, 1579 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Each composite number qrs = a(n)-1 is a squarefree 3-almost prime. This sequence is a subsequence of A078330 which, besides having 3 as its first term, first differs by including 2311 = 2*3*5*7*11 + 1 (a squarefree 5-almost prime plus 1).
LINKS
MATHEMATICA
With[{nn=50}, Take[Union[Select[Times@@@Subsets[Prime[Range[2nn]], {3}]+1, PrimeQ]], nn]] (* Harvey P. Dale, Jun 06 2021 *)
PROG
(PARI) /* Here are five equivalent PARI programs */ forprime(p=2, 2400, if(moebius(p-1)==-1 && omega(p-1)==3, print1(p, ", "))) forprime(p=2, 2400, if(moebius(p-1)==-1 && bigomega(p-1)==3, print1(p, ", "))) forprime(p=2, 2400, if(bigomega(p-1)==3 && omega(p-1)==3, print1(p, ", "))) forprime(p=2, 2400, if(omega(p-1)==3 && issquarefree(p-1), print1(p, ", "))) forprime(p=2, 2400, if(bigomega(p-1)==3 && issquarefree(p-1), print1(p, ", ")))
CROSSREFS
Cf. A078330 (primes p with mu(p-1) = -1).
Sequence in context: A069455 A211549 A118637 * A139883 A060834 A060844
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jun 18 2004
STATUS
approved

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Last modified April 21 03:11 EDT 2024. Contains 371850 sequences. (Running on oeis4.)