|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|