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

%I A294752 #22 Nov 10 2017 21:47:10
%S A294752 53295,119301,229245,399993,608235,623645,1462731,2324495,3696189,
%T A294752 3973145,4482879,5356445,5920971,6249633,7588977,8270385,10160943,
%U A294752 10450121,10505373,13185969,13630011,13760929,14935029,19095395,20280795,22566271,23131549,23408259,24778401
%N A294752 Squarefree products of k primes that are symmetrically distributed around their average. Case k = 5.
%H A294752 Robert Israel, <a href="/A294752/b294752.txt">Table of n, a(n) for n = 1..3560</a>
%e A294752 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.
%p A294752 with(numtheory): P:=proc(q,h) local a,b,k,n,ok;
%p A294752 for n from 2*3*5*7*11 to q do if not isprime(n) and issqrfree(n) then a:=ifactors(n)[2];
%p A294752 if nops(a)=h then b:=2*add(a[k][1],k=1..nops(a))/nops(a); ok:=1;
%p A294752 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);
%p A294752 # Alternative:
%p A294752 N:= 10^8: # to get all terms <= N
%p A294752 M:= floor((8*N/15)^(1/3)):
%p A294752 P:= select(isprime, [seq(i,i=3..M,2)]): nP:= nops(P):
%p A294752 Res:= NULL:
%p A294752 for i3 from 3 to nP-2 do
%p A294752   p3:= P[i3];
%p A294752   for i1 from 1 to i3-2 do
%p A294752     if isprime(2*p3 - P[i1]) then
%p A294752       for i2 from i1+1 to i3-1 do
%p A294752         if isprime(2*p3 - P[i2]) then
%p A294752           v:=P[i1]*P[i2]*p3*(2*p3-P[i2])*(2*p3-P[i1]);
%p A294752           if v <= N then Res:= Res, v fi
%p A294752         fi
%p A294752       od
%p A294752      fi
%p A294752    od
%p A294752 od:
%p A294752 sort([Res]): # _Robert Israel_, Nov 10 2017
%o A294752 (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
%Y A294752 Subsequence of A046387, A203614.
%Y A294752 Cf. A006881 (k=2), A262723 (k=3), A294751 (k=4), A294776 (k=6).
%K A294752 nonn
%O A294752 1,1
%A A294752 _Paolo P. Lava_, Nov 08 2017
%E A294752 More terms from _Giovanni Resta_, Nov 09 2017
%E A294752 Missing term 23131549 inserted by _Robert Israel_, Nov 10 2017