A123201 Numbers m such that the factorizations of m..m+7 have the same number of primes (including multiplicities).

3405122, 3405123, 6612470, 8360103, 8520321, 9306710, 10762407, 12788342, 12788343, 15212151, 15531110, 16890901, 17521382, 17521383, 21991382, 21991383, 22715270, 22715271, 22841702, 22841703, 22914722, 22914723

Offset: 1

Author

Zak Seidov, Nov 05 2006

Keywords

• nonn

Comments

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).

Examples

			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.
		

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), A123103 (k=6), this sequence (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>=7, print1(n-7 ",")), c=0; p1=p2)) \\ Donovan Johnson, Mar 20 2013

Extensions

a(7)-a(22) from Donovan Johnson, Apr 09 2010