A086263 Smaller of two consecutive squarefree numbers having equal numbers of prime factors.

2, 14, 21, 33, 34, 38, 57, 85, 86, 93, 94, 118, 122, 133, 141, 142, 145, 158, 177, 201, 202, 205, 213, 214, 217, 218, 230, 253, 285, 298, 301, 302, 326, 334, 381, 393, 394, 429, 434, 445, 446, 453, 481, 501, 514, 526, 537, 542, 553, 565, 609, 622, 633, 634

Offset: 1

Author

Reinhard Zumkeller, Jul 14 2003

Keywords

• nonn

Comments

a(k) is a term of A075039 iff a(k)+1 = a(k+1).

If a prime divides a(n) then it does not divide a(n) + 1. If a prime divides a(n) + 1, then it does not divide a(n). The sets of prime divisors of a(n) and a(n) + 1 are disjoint. - Torlach Rush, Jan 13 2018

Examples

			230 = 2*5*23 and 230+1 = 3*7*11, therefore 230 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A005117, A263990 (2 prime factors), A215217 (3 prime factors), A318896 (4 prime factors), A318964 (5 prime factors), A001221, A001222, A075039.

Programs

Mathematica

Select[Range[2, 634], SquareFreeQ[#] && SquareFreeQ[# + 1] && Length[FactorInteger[#]] == Length[FactorInteger[# + 1]] &] (* T. D. Noe, Jun 26 2013 *)
#[[1,1]]&/@Select[Partition[Table[{n,If[SquareFreeQ[n],1,0], PrimeOmega[ n]},{n,700}],2,1],#[[1,2]]==#[[2,2]]==1&&#[[1,3]]==#[[2,3]]&] (* Harvey P. Dale, Dec 13 2014 *)

PARI

for(n=1,10^3, if ( issquarefree(n) && issquarefree(n+1) && (omega(n)==omega(n+1)) , print1(n,", "))); \\ Joerg Arndt, Jun 26 2013

Formula

A001221(a(n)) = A001222(a(n)) = A001221(a(n)+1) = A001222(a(n)+1).