OFFSET
1,1
COMMENTS
The first pair of consecutive integers that are both terms is (728, 729), and the first run of three consecutive integers all appearing as terms begins at 127251 (see Examples). The first run of four consecutive integers appearing as terms begins at 4405832. Do arbitrarily long runs of consecutive integers occur?
EXAMPLE
495 = 3*3*5*11 has 4 prime factors and 12 divisors, while 496 = 2*2*2*2*31 has 5 prime factors but only 10 divisors, so 495 is a term.
728 = 2*2*2*7*13, 729 = 3*3*3*3*3*3, and 730 = 2*5*73 have 5, 6, and 3 prime factors and 16, 7, and 8 divisors, respectively, so both 728 and 729 are terms.
127251 = 3*3*3*3*1571, 127252 = 2*2*29*1097, 127253 = 7*7*7*7*53, and 127254 = 2*3*127*167 have 5, 4, 5, and 4 prime factors, and 10, 12, 10, and 16 divisors, respectively, so 127251, 127252, and 127253 are all terms.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, May 14 2023
STATUS
approved