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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).
1
1, 15, 20, 30, 35, 50, 112, 143, 168, 189, 252, 280, 315, 323, 378, 392, 420, 441, 525, 588, 630, 700, 735, 882, 899, 980, 1029, 1050, 1372, 1470, 1750, 1763, 2058, 2450, 2816, 3430, 3599, 3773, 4224, 4802, 5183, 5929, 6336, 7040, 9317, 9504, 9856, 10403
OFFSET
1,2
LINKS
EXAMPLE
112 is a term because 112 = 2^4*7 with 5 primes dividing it and 7-2=5.
MATHEMATICA
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 *)
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Aug 02 2003
EXTENSIONS
Name edited by Hugo Pfoertner, Dec 16 2019
STATUS
approved