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 A294751 Squarefree products of k primes that are symmetrically distributed around their average. Case k = 4. 4
 2145, 4641, 4845, 5005, 9177, 11305, 13485, 13585, 17017, 21489, 21505, 23529, 26445, 31465, 31857, 33649, 35409, 35581, 36685, 42441, 43401, 46189, 46345, 49569, 50065, 53985, 60697, 61705, 63085, 63597, 65569, 67821, 69745, 77745, 80845, 83049, 87505, 88881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 2145 = 3*5*11*13. Prime factors average is (3 + 5 + 11 + 13)/4 = 8 and 3 + 5 = 8 = 13 - 5, 5 + 3 = 8 = 11 - 3. MAPLE with(numtheory): P:=proc(q, h) local a, b, k, n, ok; for n from 2*3*5*7 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, 4); # Alternative: N:= 10^5: # to get terms <= N M:= floor(max(fsolve(3*5*(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))^2 >= 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) >= N then break fi;       if not isprime(m-y) then next fi;       Res:= Res, x*(m-x)*y*(m-y); od od od: sort([Res]); # Robert Israel, May 19 2019 PROG (PARI) isok(n, nb=4) = {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 A046386. Cf. A006881 (k=2), A262723 (k=3), A294752 (k=5), A294776 (k=6). Sequence in context: A179271 A118576 A259413 * A251893 A251870 A291135 Adjacent sequences:  A294748 A294749 A294750 * A294752 A294753 A294754 KEYWORD nonn AUTHOR Paolo P. Lava, Nov 08 2017 EXTENSIONS More terms from Giovanni Resta, Nov 09 2017 STATUS approved

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Last modified July 7 12:47 EDT 2022. Contains 355148 sequences. (Running on oeis4.)