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

1,1

Comments

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

Links

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

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

Adjacent sequences: A123100 A123101 A123102 * A123104 A123105 A123106

Keyword

nonn

Author

Zak Seidov, Nov 05 2006

Extensions

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

Status

approved