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A123103
Numbers m such that the factorizations of m..m+6 have the same number of primes (including multiplicities).
12
211673, 298433, 355923, 381353, 460801, 506521, 540292, 568729, 690593, 705953, 737633, 741305, 921529, 1056529, 1088521, 1105553, 1141985, 1187121, 1362313, 1721522, 1811704, 1828070, 2016721, 2270633, 2369809, 2535721, 2590985
OFFSET
1,1
COMMENTS
Subset of A045940, Numbers m such that the factorizations of m..m+3 have the same number of primes (including multiplicities).
LINKS
EXAMPLE
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.
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).
PROG
(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 */
CROSSREFS
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).
Sequence in context: A340158 A097021 A236086 * A259756 A251511 A252880
KEYWORD
nonn
AUTHOR
Zak Seidov, Nov 05 2006
EXTENSIONS
a(14)-a(27) from Donovan Johnson, Mar 26 2010
STATUS
approved