A294776 Squarefree products of k primes that are symmetrically distributed around their average. Case k = 6.

1616615, 3411705, 7436429, 9408035, 10163195, 12838371, 13037385, 13844919, 14969435, 19605131, 20414121, 23783045, 24997749, 25113935, 27568145, 30478565, 31473255, 32518535, 33999455, 39946569, 43134015, 46115135, 48215255, 50907855, 56179409, 61558343

Offset: 1

Author

Paolo P. Lava, Nov 09 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A067885.

Cf. A006881 (k=2), A262723 (k=3), A294751 (k=4), A294752 (k=5).

Programs

Maple

with(numtheory): P:=proc(q,h) local a,b,k,n,ok;
for n from 2*3*5*7*11*13 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(10^9,6);
# Alternative:
N:= 10^8: # to get all terms <= N
M:= floor(fsolve(3*5*7*(M-7)*(M-5)*(M-3) = N)):
P:= select(isprime, [seq(i,i=3..M/2,2)]): nP:= nops(P):
Res:= NULL:
for m from 10 by 2 to M do
  for ix from 1 to nP-2 do
    x:= P[ix];
    if x >= m/2 or (x*(m-x))^3 >= N then break fi;
    if not isprime(m-x) then next fi;
    for iy from ix+1 to nP-1 do
      y:= P[iy];
      if y >= m/2 or x*(m-x)*(y*(m-y))^2 >= N then break fi;
      if not isprime(m-y) then next fi;
      for iz from iy+1 to nP do
        z:= P[iz];
        if z >= m/2 then break fi;
        v:= x*(m-x)*y*(m-y)*z*(m-z);
        if v > N then break fi;
        if isprime(m-z) then Res:= Res, v fi;
od od od od:
sort([Res]); # Robert Israel, May 19 2019

PARI

isok(n, nb=6) = {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