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A086263 Smaller of two consecutive squarefree numbers having equal numbers of prime factors. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

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

MAPLE

with(numtheory); P:=proc(q, h) local a, b, n; for n from 1 to q do

a:=ifactors(n)[2]; if nops(a)=2 then if a[1][2]=1 and a[2][2]=1 then

b:=ifactors(n+h)[2]; if nops(b)=2 then if b[1][2]=1 and b[2][2]=1 then print(n); fi; fi; fi; fi; od; end: P(10^6, 1); # Paolo P. Lava, Jun 26 2013

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A140578 A052213 A280074 * A355709 A335071 A073143

Adjacent sequences:  A086260 A086261 A086262 * A086264 A086265 A086266

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 14 2003

STATUS

approved

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Last modified September 29 17:46 EDT 2022. Contains 357090 sequences. (Running on oeis4.)