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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.

%I A298045 #13 Jan 19 2018 09:20:07
%S A298045 1,60,300,504,1500,1512,3528,3660,4536,7500,12240,13608,24696,36720,
%T A298045 37500,40824,122472,172872,187500,208080,223260,367416,937500,1102248,
%U A298045 1210104,3306744,3537360,4687500,8470728,9920232,12450312,13618860,23437500,29760696
%N 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.
%C A298045 Subset of A060765.
%C A298045 Fixed points of A060766.
%C A298045 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
%C A298045 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
%H A298045 Giovanni Resta, <a href="/A298045/b298045.txt">Table of n, a(n) for n = 1..61</a> (terms < 1.5*10^11)
%e A298045 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.
%e A298045 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.
%e A298045 lcm(1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 42, 84, 252) is 504 again.
%p A298045 with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=sort([op(divisors(n))]);
%p A298045 if n=lcm(op([seq(a[k+1]-a[k],k=1..nops(a)-1)])) then print(n); fi; od; end: P(10^6);
%t A298045 {1}~Join~Select[Range[2, 10^6], LCM @@ Differences@ Divisors@ # == # &] (* _Michael De Vlieger_, Jan 13 2018 *)
%Y A298045 Cf. A060765, A060766.
%K A298045 nonn
%O A298045 1,2
%A A298045 _Paolo P. Lava_, Jan 11 2018
%E A298045 More terms from _Michael De Vlieger_, Jan 13 2018
%E A298045 a(31)-a(34) from _Giovanni Resta_, Jan 15 2018