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A221280 Numbers m such that lambda(m) = lambda(m+1), where lambda(n) = A008836(n) is the Liouville function. 3
2, 7, 9, 11, 12, 14, 15, 17, 18, 19, 21, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 38, 39, 41, 42, 43, 44, 47, 52, 54, 55, 56, 57, 64, 66, 67, 70, 71, 72, 75, 78, 79, 81, 84, 85, 86, 87, 90, 93, 94, 95, 97, 98, 101, 102, 107, 108, 109, 112, 113, 116, 118, 121, 122, 124, 127, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence is infinite. Density is conjecturally 1/2; it is easy to show that the density is at least 1/4 (one of k, 2k, and 2k+1 is in this sequence).

m is a term iff lambda(A000217(m)) = -1. See link. - Jon Maiga, Jan 03 2019

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

J. Maiga, Liouville's function and triangular numbers, 2018.

MATHEMATICA

Select[ Range[130], LiouvilleLambda[#] == LiouvilleLambda[# + 1] &] (* Jean-Fran├žois Alcover, Jul 30 2013 *)

PROG

(PARI) is(n)=(-1)^bigomega(n)==(-1)^bigomega(n+1)

CROSSREFS

Cf. A000217, A008836, A221281, A221282.

Sequence in context: A073074 A034796 A047526 * A166570 A003668 A191263

Adjacent sequences:  A221277 A221278 A221279 * A221281 A221282 A221283

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Jan 09 2013

STATUS

approved

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)