A023575 -id:A023575 - cp's OEIS frontend

A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

0, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 2, 4, 2, 3, 2, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 4, 4, 3, 4, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 4

Offset: 1

Clark Kimberling

nonn

This is taking prime(0)=1 (see first comment in A023515). - Vincenzo Librandi, Apr 27 2019

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A023515, A023524, A023568, A023575, A023582, A023589.

[#PrimeDivisors(NthPrime(n)*(NthPrime(n-1))-1): n in [1..100]]; // Vincenzo Librandi, Apr 27 2019

0,seq(nops(numtheory:-factorset(ithprime(n)*ithprime(n-1)-1)),n=2..120); # Muniru A Asiru, Apr 29 2019

Prepend[Table[PrimeNu[Prime[n] Prime[n-1] - 1], {n, 2, 80}],0] (* Vincenzo Librandi, Apr 27 2019 *)

a(n) = if (n==1, 0, omega(prime(n)*prime(n-1) - 1)); \\ Michel Marcus, Apr 30 2019

a(n) = A001221(A023515(n)).

A352163 a(n) is the least prime p such that p+3 is divisible by exactly n distinct primes.

Original entry on oeis.org

2, 3, 67, 907, 10007, 170167, 3233227, 74364287, 2156564407, 79792883167, 2874700358527, 106363913265607, 4999103923483667, 204963260862830467, 15485628496253425507, 640920116718070879687, 45505328286983032457987, 3048856995227863174685327, 191219157742953165026391187, 14692441860003072638808605267

Offset: 1

Robert Israel, Mar 06 2022

nonn

For n>2, a(n) = A002110(n+1)/3-3 if that is prime. This occurs for n = 3, 5, 6, 7, 8, 9, 14, 16, 46, 47, 70, 101, 113, 168, 175, 200, ...

			a(4) = 907 because 907 is prime and 907+3 = 910 = 2*5*7*13 has 4 prime divisors.

Cf. A002110, A023575.

f:= proc(p) nops(numtheory:-factorset(p+3)) end proc:
V:= Vector(8): count:= 0:
p:= 1:
while count < 8 do
  p:= nextprime(p);
  v:= f(p);
  if V[v] = 0 then V[v]:= p; count:= count+1; fi
od:
convert(V,list);

More terms from David A. Corneth, Mar 06 2022

cp's OEIS Frontend

A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

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