

A273131


Numbers n such that the bottom entry of the difference table of the divisors of n divides n.


1



1, 2, 4, 6, 8, 12, 14, 16, 24, 32, 64, 128, 152, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648
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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 nonpowers 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, nd1, vd = vector(#vd1, 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(#d1, i1)*(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(m1, 1, 1) :
T[mk, k] = T[mk1, k+1]  T[mk1, k]
return T[len(D)1, 0].divides(n)
print filter(is_A273131, range(1, 6000)) # Peter Luschny, May 18 2016


CROSSREFS

Cf. A000079, A027750, A187202, A273102, A273103, A273109.
Sequence in context: A043756 A043765 A043569 * A249721 A010063 A260652
Adjacent sequences: A273128 A273129 A273130 * A273132 A273133 A273134


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



