A136349
Numbers k of the form Product_{j=1..m} prime(j) such that k-1 is prime.
Original entry on oeis.org
6, 30, 2310, 30030, 304250263527210, 23768741896345550770650537601358310
Offset: 1
a(3)=30 where the prime factors are 2,3,5; since N-1=29, prime, N=30 is added to the sequence.
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Select[FoldList[Times,1,Prime[Range[70]]],PrimeQ[#-1]&] (* Harvey P. Dale, Jan 09 2011 *)
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c=0;t=1;vector(7,n,until( ispseudoprime( -1+t*=prime(c++)),);t)
A136351
Primorial numbers p# such that p# + 1 is a prime.
Original entry on oeis.org
1, 2, 6, 30, 210, 2310, 200560490130
Offset: 1
a(6)=2310 is followed by prime 2311 whereas 30030 is not followed by a prime.
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Select[FoldList[Times, 1, Prime[Range[18]]],PrimeQ[#+1]&] (* James C. McMahon, May 08 2025 *)
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S=[];for(n=0, 80, k=vecprod(primes(n)); if(isprime(k+1), S=concat(S,k))); S \\ Miles Englezou, Oct 28 2024
Changed a(1) from 4 to 2 and edited by
R. J. Mathar, Jul 23 2008
A136352
Primorials P for which neither P-1 nor P+1 is prime.
Original entry on oeis.org
510510, 9699690, 223092870, 6469693230, 7420738134810, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070, 117288381359406970983270, 7858321551080267055879090
Offset: 1
13# = 30030 is preceded by a prime but is not followed by a prime. 17# = 510510 is neither preceded nor followed by a prime.
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Select[FoldList[Times, 1, Prime[Range[19]]],!PrimeQ[#+1]&&!PrimeQ[#-1]&] (* James C. McMahon, May 08 2025 *)
A136350
Primorial numbers #p such that (#p)-1 is composite.
Original entry on oeis.org
210, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070, 117288381359406970983270
Offset: 1
a(1)=210 because 209=A002110(4)-1 is not prime.
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Select[FoldList[Times, 1, Prime[Range[18]]],CompositeQ[#-1]&] (* James C. McMahon, May 08 2025 *)
A231209
Smallest squarefree number k with 2^n ways to write k as k = x*y, where x, y = squarefree numbers, 1 <= x <= y <= k.
Original entry on oeis.org
1, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070
Offset: 0
a(0)=1 because squarefree number k=1 with 2^0=1 way to write k = x*y = 1*1 where x=1 and y=1 are squarefree numbers;
a(1)=6 because squarefree number k=6 with 2^1=2 ways to write k = x*y = 1*6 = 2*3 where 1, 6, 2, 3, are all squarefree numbers;
a(2)=30 because squarefree number k=30 with 2^2=4 ways to write k = 1*30 = 2*15 = 3*10 = 5*6 where 1, 30, 2, 15, 3, 10, 5, 6 are all squarefree numbers;
a(3)=210 because squarefree number k=210 with 2^3=8 ways to write k = 1*210 = 2*105 = 3*70 = 5*42 = 6*35 = 7*30 = 10*21 = 14*15 where 1, 210, 2, 105, 3, 70, 5, 42, 6, 35, 7, 30, 10, 21, 14, 15 are all squarefree numbers.
Showing 1-5 of 5 results.
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