A294752 Squarefree products of k primes that are symmetrically distributed around their average. Case k = 5.

53295, 119301, 229245, 399993, 608235, 623645, 1462731, 2324495, 3696189, 3973145, 4482879, 5356445, 5920971, 6249633, 7588977, 8270385, 10160943, 10450121, 10505373, 13185969, 13630011, 13760929, 14935029, 19095395, 20280795, 22566271, 23131549, 23408259, 24778401

Offset: 1

Author

Paolo P. Lava, Nov 08 2017

Keywords

• nonn

Examples

			53295 = 3*5*11*17*19. Prime factors average is (3 + 5 + 11 + 17 + 19)/5 = 11 and 3 + 8 = 11 = 19 - 8, 5 + 6 = 11 = 17 - 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3560

Crossrefs

Subsequence of A046387, A203614.

Cf. A006881 (k=2), A262723 (k=3), A294751 (k=4), A294776 (k=6).

Programs

Maple

with(numtheory): P:=proc(q,h) local a,b,k,n,ok;
for n from 2*3*5*7*11 to q do if not isprime(n) and issqrfree(n) then a:=ifactors(n)[2];
if nops(a)=h then b:=2*add(a[k][1],k=1..nops(a))/nops(a); ok:=1;
for k from 1 to trunc(nops(a)/2) do if a[k][1]+a[nops(a)-k+1][1]<>b then ok:=0; break; fi; od; if ok=1 then print(n); fi; fi; fi; od; end: P(10^9,5);
# Alternative:
N:= 10^8: # to get all terms <= N
M:= floor((8*N/15)^(1/3)):
P:= select(isprime, [seq(i,i=3..M,2)]): nP:= nops(P):
Res:= NULL:
for i3 from 3 to nP-2 do
  p3:= P[i3];
  for i1 from 1 to i3-2 do
    if isprime(2*p3 - P[i1]) then
      for i2 from i1+1 to i3-1 do
        if isprime(2*p3 - P[i2]) then
          v:=P[i1]*P[i2]*p3*(2*p3-P[i2])*(2*p3-P[i1]);
          if v <= N then Res:= Res, v fi
        fi
      od
     fi
   od
od:
sort([Res]): # Robert Israel, Nov 10 2017

PARI

isok(n, nb=5) = {if (issquarefree(n) && (omega(n)==nb), f = factor(n)[, 1]~; avg = vecsum(f)/#f; for (k=1, #f\2, if (f[k] + f[#f-k+1] != 2*avg, return(0));); return (1););} \\ Michel Marcus, Nov 10 2017

Extensions

More terms from Giovanni Resta, Nov 09 2017

Missing term 23131549 inserted by Robert Israel, Nov 10 2017