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, 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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A001222, A006530, A046665.

Sequence in context: A120159 A163602 A074236 * A111200 A088494 A109659

Adjacent sequences: A086767 A086768 A086769 * A086771 A086772 A086773

Keyword

nonn

Author

Jason Earls, Aug 02 2003

Extensions

Name edited by Hugo Pfoertner, Dec 16 2019

Status

approved