A123103 Numbers m such that the factorizations of m..m+6 have the same number of primes (including multiplicities).

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

Author

Zak Seidov, Nov 05 2006

Keywords

• nonn

Comments

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

Examples

			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).
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000

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).

Programs

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 */

Extensions

a(14)-a(27) from Donovan Johnson, Mar 26 2010