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

1,1

Links

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

Example

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.

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

Prog

(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

Crossrefs

Subsequence of A046387, A203614.

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

Sequence in context: A061330 A195656 A195651 * A164519 A237180 A186199

Adjacent sequences: A294749 A294750 A294751 * A294753 A294754 A294755

Keyword

nonn

Author

Paolo P. Lava, Nov 08 2017

Extensions

More terms from Giovanni Resta, Nov 09 2017

Missing term 23131549 inserted by Robert Israel, Nov 10 2017

Status

approved