

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Cf. A060765, A060766.
Sequence in context: A179811 A268805 A146750 * A063497 A096363 A033591
Adjacent sequences: A298042 A298043 A298044 * A298046 A298047 A298048


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



