OFFSET
1,2
COMMENTS
All powers of 2 are in the sequence because the bottom entries of their difference triangles are always 1's.
Besides 6, 12, 14, 24 and 152, are there any other non-powers of 2 in this sequence? - David A. Corneth, May 19 2016
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..40
EXAMPLE
For n = 14 the difference triangle of the divisors of 14 is
1 . 2 . 7 . 14
. 1 . 5 . 7
. . 4 . 2
. . .-2
The bottom entry is -2 and -2 divides 14, so 14 is in the sequence.
MATHEMATICA
Select[Range[10^6], Function[k, If[k == {0}, False, Divisible[#, First@ k]]]@ NestWhile[Differences, Divisors@ #, Length@ # > 1 &] &] (* Michael De Vlieger, May 17 2016 *)
PROG
(PARI) isok(n) = {my(d = divisors(n)); my(nd = #d); my(vd = d); for (k=1, nd-1, vd = vector(#vd-1, j, vd[j+1] - vd[j]); ); vd[1] && ((n % vd[1]) == 0); } \\ Michel Marcus, May 16 2016
(PARI) is(n) = my(d=divisors(n), s=sum(i=1, #d, binomial(#d-1, i-1)*(-1)^i*d[i])); if(s!=0, n%s==0) \\ David A. Corneth, May 19 2016
(Sage)
def is_A273131(n):
D = divisors(n)
T = matrix(ZZ, len(D))
for m, d in enumerate(D):
T[0, m] = d
for k in range(m-1, -1, -1) :
T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k]
return T[len(D)-1, 0].divides(n)
print([n for n in range(1, 6000) if is_A273131(n)])
# Peter Luschny, May 18 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 16 2016
EXTENSIONS
a(12) = 128 and a(14)-a(25) from Michel Marcus, May 16 2016
a(26)-a(28) from David A. Corneth, May 19 2016
a(29)-a(37) from Lars Blomberg, Oct 18 2016
STATUS
approved