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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 21 09:19 EDT 2022. Contains 353908 sequences. (Running on oeis4.)