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A298045
Integers equal to the least common multiple of the set of numbers generated by all the differences between their consecutive divisors, taken in increasing order.
1
1, 60, 300, 504, 1500, 1512, 3528, 3660, 4536, 7500, 12240, 13608, 24696, 36720, 37500, 40824, 122472, 172872, 187500, 208080, 223260, 367416, 937500, 1102248, 1210104, 3306744, 3537360, 4687500, 8470728, 9920232, 12450312, 13618860, 23437500, 29760696
OFFSET
1,2
COMMENTS
Subset of A060765.
Fixed points of A060766.
Many terms m > 1 have omega(m) = 3 or 4, 60 and 3660 being the smallest of both, respectively. Is there a term with omega(m) = 5? - Michael De Vlieger, Jan 13 2018
The first two terms with 5 prime divisors are 149829840 and 1348395120. The sequence is infinite since it contains all the numbers of the form 72*7^k, for k>0. - Giovanni Resta, Jan 15 2018
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..61 (terms < 1.5*10^11)
EXAMPLE
Divisors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252 and 504.
Differences are: 2 - 1 = 1, 3 - 2 = 1, 4 - 3 = 1, 6 - 4 = 2, 7 - 6 = 1, 8 - 7 = 1, 9 - 8 = 1, 12 - 9 = 3, 14 - 12 = 2, 18 - 14 = 4, 21 - 18 = 3, 24 - 21 = 3, 28 - 24 = 4, 36 - 28 = 8, 42 - 36 = 6, 56 - 42 = 14, 63 - 56 = 7, 72 - 63 = 9, 84 - 72 = 12, 126 - 84 = 42, 168 - 126 = 42, 252 - 168 = 84, 504 - 252 = 252.
lcm(1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 42, 84, 252) is 504 again.
MAPLE
with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do a:=sort([op(divisors(n))]);
if n=lcm(op([seq(a[k+1]-a[k], k=1..nops(a)-1)])) then print(n); fi; od; end: P(10^6);
MATHEMATICA
{1}~Join~Select[Range[2, 10^6], LCM @@ Differences@ Divisors@ # == # &] (* Michael De Vlieger, Jan 13 2018 *)
CROSSREFS
Sequence in context: A179811 A268805 A146750 * A063497 A096363 A033591
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jan 11 2018
EXTENSIONS
More terms from Michael De Vlieger, Jan 13 2018
a(31)-a(34) from Giovanni Resta, Jan 15 2018
STATUS
approved