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A086770 Numbers k such that the difference between the largest and the smallest prime divisor of k equals the number of prime divisors of k (counted with multiplicity).

%I A086770 #23 Sep 08 2022 08:45:11
%S A086770 1,15,20,30,35,50,112,143,168,189,252,280,315,323,378,392,420,441,525,
%T A086770 588,630,700,735,882,899,980,1029,1050,1372,1470,1750,1763,2058,2450,
%U A086770 2816,3430,3599,3773,4224,4802,5183,5929,6336,7040,9317,9504,9856,10403
%N A086770 Numbers k such that the difference between the largest and the smallest prime divisor of k equals the number of prime divisors of k (counted with multiplicity).
%H A086770 Amiram Eldar, <a href="/A086770/b086770.txt">Table of n, a(n) for n = 1..10000</a>
%e A086770 112 is a term because 112 = 2^4*7 with 5 primes dividing it and 7-2=5.
%t A086770 seqQ[1] = True; seqQ[n_] := Plus @@ Last /@ (f = FactorInteger[n]) == f[[-1, 1]] - f[[1, 1]]; Select[Range[10^4], seqQ] (* _Amiram Eldar_, Dec 16 2019 *)
%o A086770 (Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [1] cat [k:k in [2..10000]| Max(PrimeDivisors(k))-Min(PrimeDivisors(k)) eq f(k)]; // _Marius A. Burtea_, Dec 16 2019
%o A086770 (PARI) print1("1, "); for(k=2,10500,my(f=factor(k));if(bigomega(k)==vecmax(f[, 1])-f[1,1],print1(k,", "))) \\ _Hugo Pfoertner_, Dec 16 2019
%Y A086770 Cf. A001222, A006530, A046665.
%K A086770 nonn
%O A086770 1,2
%A A086770 _Jason Earls_, Aug 02 2003
%E A086770 Name edited by _Hugo Pfoertner_, Dec 16 2019