A354949 a(n) is the first interprime that is divisible by exactly n squares of primes.

6, 4, 72, 3528, 108900, 12744900, 3852664200, 260620460100, 282251958288300

Offset: 0

Author

J. M. Bergot and Robert Israel, Jun 13 2022

Keywords

• nonn
• more

Comments

a(n) is the first member k of A024675 such that A056170(k) = n.

Examples

			a(2) = 72: 72 is an interprime because 72 = (71+73)/2 with 71 and 73 consecutive primes; 72 is divisible by the two squares of primes 2^2 and 3^2; and no smaller interprime is divisible by two squares of primes.
		

Crossrefs

Cf. A024675, A056170

Programs

Maple

f:= proc(n) local F,t;
  F:= ifactors(n)[2];
  nops(select(t -> t[2]>=2, F))
end proc:
V:= Array(0..5,-1): count:= 0: q:= 3:
while count < 6 do
  p:= q; q:= nextprime(q); x:= (p+q)/2;
  v:= f(x);
  if V[v] = -1 then V[v]:= x; count:= count+1 fi
od:
convert(V,list):

Extensions

a(6) from Amiram Eldar, Jun 13 2022