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, 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

Author

Paolo P. Lava, Jan 11 2018

Keywords

• nonn

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

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..61 (terms < 1.5*10^11)

Crossrefs

Cf. A060765, A060766.

Programs

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 *)

Extensions

More terms from Michael De Vlieger, Jan 13 2018

a(31)-a(34) from Giovanni Resta, Jan 15 2018