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A294776 Squarefree products of k primes that are symmetrically distributed around their average. Case k = 6. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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

PROG

(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

CROSSREFS

Subsequence of A067885.

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

Sequence in context: A235174 A234410 A069374 * A103793 A064117 A173428

Adjacent sequences:  A294773 A294774 A294775 * A294777 A294778 A294779

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Nov 09 2017

EXTENSIONS

More terms from Giovanni Resta, Nov 09 2017

STATUS

approved

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Last modified August 14 06:25 EDT 2020. Contains 336477 sequences. (Running on oeis4.)