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
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