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%I #21 Feb 11 2023 22:40:33
%S 3405122,3405123,6612470,8360103,8520321,9306710,10762407,12788342,
%T 12788343,15212151,15531110,16890901,17521382,17521383,21991382,
%U 21991383,22715270,22715271,22841702,22841703,22914722,22914723
%N Numbers m such that the factorizations of m..m+7 have the same number of primes (including multiplicities).
%C Note that because 3405130 = 2*5*167*2039 is also the product of 4 primes, 3405122 is the first m such that numbers m..m+8 are products of the same number k of primes (k=4).
%H Donovan Johnson, <a href="/A123201/b123201.txt">Table of n, a(n) for n = 1..10000</a>
%e 3405122 = 2*7*29*8387, 3405123 = 3^2*19*19913, 3405124 = 2^2*127*6703, 3405125 = 5^3*27241, 3405126 = 2*3*59*9619, 3405127 = 11*23*43*313, 3405128 = 2^3*425641, 3405129 = 3*7*13*12473 all products of 4 primes.
%o (PARI) c=0; p1=0; for(n=2, 10^8, p2=bigomega(n); if(p1==p2, c++; if(c>=7, print1(n-7 ",")), c=0; p1=p2)) \\ _Donovan Johnson_, Mar 20 2013
%Y Numbers m through m+k have the same number of prime divisors (with multiplicity): A045920 (k=1), A045939 (k=2), A045940 (k=3), A045941 (k=4), A045942 (k=5), A123103 (k=6), this sequence (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 05 2006
%E a(7)-a(22) from _Donovan Johnson_, Apr 09 2010