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A294752
Squarefree products of k primes that are symmetrically distributed around their average. Case k = 5.
4
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
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
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