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

1,1

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).

Links

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

Example

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.

Prog

(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

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).

Sequence in context: A206382 A114682 A157106 * A358017 A258517 A258510

Adjacent sequences: A123198 A123199 A123200 * A123202 A123203 A123204

Keyword

nonn

Author

Zak Seidov, Nov 05 2006

Extensions

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

Status

approved