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Numbers m such that the factorizations of m..m+6 have the same number of primes (including multiplicities).
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%I #17 Feb 11 2023 22:52:33

%S 211673,298433,355923,381353,460801,506521,540292,568729,690593,

%T 705953,737633,741305,921529,1056529,1088521,1105553,1141985,1187121,

%U 1362313,1721522,1811704,1828070,2016721,2270633,2369809,2535721,2590985

%N Numbers m such that the factorizations of m..m+6 have the same number of primes (including multiplicities).

%C Subset of A045940, Numbers m such that the factorizations of m..m+3 have the same number of primes (including multiplicities).

%H Donovan Johnson, <a href="/A123103/b123103.txt">Table of n, a(n) for n = 1..10000</a>

%e 211673 = 7*11*2749, 211674 = 2*3*35279, 211675 = 5^2*8467, 211676 = 2^2*52919, 211677 = 3*37*1907, 211678 = 2*109*971, 211679 = 13*19*857 are all triprimes.

%e 355923 = 3^2*71*557, 355924 = 2^2*101*881, 355925 = 5^2*23*619, 355926 = 2*3*137*433, 355927 = 11*13*19*131, 355928 = 2^3*44491, 355929 = 3*7*17*997 are all products of 4 primes (typo corrected _Zak Seidov_, Oct 24 2022).

%o (PARI) c=0; p1=0; for(n=2, 10^8, p2=bigomega(n); if(p1==p2, c++; if(c>=6, print1(n-6 ",")), 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), this sequence (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 05 2006

%E a(14)-a(27) from _Donovan Johnson_, Mar 26 2010