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Numbers m such that the factorizations of m..m+8 have the same number of primes (including multiplicities).
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%I #8 Feb 11 2023 22:40:37

%S 3405122,12788342,17521382,21991382,22715270,22841702,22914722,

%T 23553171,27451669,27793334,49361762,49799889,49799890,50727123,

%U 51359029,52154450,53758502,57379970,60975410,60975411,75638644,76502870,76724630,85432322

%N Numbers m such that the factorizations of m..m+8 have the same number of primes (including multiplicities).

%H Charles R Greathouse IV, <a href="/A358017/b358017.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) list(lim)=my(v=List(),ct,cur); forfactored(n=3405122,lim\1+8, my(t=bigomega(n)); if(t==cur, if(ct++>7, listput(v,n[1]-8)), cur=t; ct=0)); Vec(v)

%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), A123201 (k=7), this sequence (k=8), A358018 (k=9), A358019 (k=10).

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Oct 24 2022