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

%I A294776 #15 May 20 2019 02:44:45
%S A294776 1616615,3411705,7436429,9408035,10163195,12838371,13037385,13844919,
%T A294776 14969435,19605131,20414121,23783045,24997749,25113935,27568145,
%U A294776 30478565,31473255,32518535,33999455,39946569,43134015,46115135,48215255,50907855,56179409,61558343
%N A294776 Squarefree products of k primes that are symmetrically distributed around their average. Case k = 6.
%H A294776 Robert Israel, <a href="/A294776/b294776.txt">Table of n, a(n) for n = 1..10000</a>
%p A294776 with(numtheory): P:=proc(q,h) local a,b,k,n,ok;
%p A294776 for n from 2*3*5*7*11*13 to q do if not isprime(n) and issqrfree(n) then a:=ifactors(n)[2];
%p A294776 if nops(a)=h then b:=2*add(a[k][1],k=1..nops(a))/nops(a); ok:=1;
%p A294776 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);
%p A294776 # Alternative:
%p A294776 N:= 10^8: # to get all terms <= N
%p A294776 M:= floor(fsolve(3*5*7*(M-7)*(M-5)*(M-3) = N)):
%p A294776 P:= select(isprime, [seq(i,i=3..M/2,2)]): nP:= nops(P):
%p A294776 Res:= NULL:
%p A294776 for m from 10 by 2 to M do
%p A294776   for ix from 1 to nP-2 do
%p A294776     x:= P[ix];
%p A294776     if x >= m/2 or (x*(m-x))^3 >= N then break fi;
%p A294776     if not isprime(m-x) then next fi;
%p A294776     for iy from ix+1 to nP-1 do
%p A294776       y:= P[iy];
%p A294776       if y >= m/2 or x*(m-x)*(y*(m-y))^2 >= N then break fi;
%p A294776       if not isprime(m-y) then next fi;
%p A294776       for iz from iy+1 to nP do
%p A294776         z:= P[iz];
%p A294776         if z >= m/2 then break fi;
%p A294776         v:= x*(m-x)*y*(m-y)*z*(m-z);
%p A294776         if v > N then break fi;
%p A294776         if isprime(m-z) then Res:= Res, v fi;
%p A294776 od od od od:
%p A294776 sort([Res]); # _Robert Israel_, May 19 2019
%o A294776 (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
%Y A294776 Subsequence of A067885.
%Y A294776 Cf. A006881 (k=2), A262723 (k=3), A294751 (k=4), A294752 (k=5).
%K A294776 nonn
%O A294776 1,1
%A A294776 _Paolo P. Lava_, Nov 09 2017
%E A294776 More terms from _Giovanni Resta_, Nov 09 2017