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A045920 Numbers n such that factorizations of n and n+1 have the same number of primes (including multiplicities). 26
2, 9, 14, 21, 25, 27, 33, 34, 38, 44, 57, 75, 85, 86, 93, 94, 98, 116, 118, 121, 122, 124, 133, 135, 141, 142, 145, 147, 153, 158, 164, 170, 171, 174, 177, 201, 202, 205, 213, 214, 217, 218, 230, 244, 245, 253, 284, 285, 296, 298, 301, 302, 326, 332, 334, 350, 356, 361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A115186 is a subsequence: A001222(A115186(n))=A001222(A115186(n)+1)=n. - Reinhard Zumkeller, Jan 16 2006

Indices k such that A076191(k) = 0. - Ray Chandler, Dec 10 2008

A045939 is a subsequence. - Zak Seidov, Jul 02 2020

This sequence is infinite (Heath-Brown, 1984). - Amiram Eldar, Jul 11 2020

REFERENCES

C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 250

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. R. Heath-Brown, A parity problem from sieve theory, Mathematika, Vol. 29, No. 1 (1982), pp. 1-6.

D. R. Heath-Brown, The divisor function at consecutive integers, Mathematika, Vol. 31, No. 1 (1984), pp. 141-149.

Adolf Hildebrand, The divisor function at consecutive integers, Pacific journal of mathematics, Vol. 129, No. 2 (1987), pp. 307-319.

FORMULA

a(n) = A278291(n) - 1. - Zak Seidov, Nov 17 2018

MATHEMATICA

f[n_]:=Plus@@Last/@FactorInteger[n]; lst={}; Do[If[f[n]==f[n+1], AppendTo[lst, n]], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)

Transpose[Transpose[Select[Partition[Table[{n, PrimeOmega[n]}, {n, 400}], 2, 1], #[[1, 2]]==#[[2, 2]]&]][[1]]][[1]] (* Harvey P. Dale, Feb 21 2012 *)

Position[Differences[PrimeOmega[Range[400]]], 0] // Flatten (* Zak Seidov, Oct 30 2012 *)

PROG

(Haskell)

import Data.List (elemIndices)

a045920 n = a045920_list !! (n-1)

a045920_list = map (+ 1) $ elemIndices 0 a076191_list

-- Reinhard Zumkeller, Mar 23 2012, Oct 11 2011

(PARI) is(n)=bigomega(n)==bigomega(n+1) \\ Charles R Greathouse IV, Sep 14 2015

CROSSREFS

Sequence in context: A274133 A288483 A304807 * A242466 A071344 A224855

Adjacent sequences:  A045917 A045918 A045919 * A045921 A045922 A045923

KEYWORD

nice,nonn

AUTHOR

Felice Russo

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified June 22 13:46 EDT 2021. Contains 345380 sequences. (Running on oeis4.)