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Snumbers

Snumbers are a class of natural numbers defined in recreational mathematics as those that can be written as the sum of two or more consecutive positive integers. For example, 9 = 4 + 5, 15 = 7 + 8 or 1 + 2 + 3 + 4 + 5, and 21 = 10 + 11 or 6 + 7 + 8. In contrast, numbers such as 1, 2, 4, 8, 16 and other powers of two cannot be expressed as such sums.

A key property of snumbers is a simple characterization: they are exactly the positive integers that are

The concept is primarily used in puzzles and recreational contexts. In practice, most integers that are not

See also: sums of consecutive integers, triangular numbers, odd divisors.

not
powers
of
two.
This
follows
from
a
classical
result
in
number
theory,
which
states
that
a
positive
integer
can
be
written
as
a
sum
of
consecutive
positive
integers
if
and
only
if
it
has
an
odd
divisor
greater
than
1.
Powers
of
two
have
no
such
divisors,
hence
they
have
no
representation
with
at
least
two
terms.
powers
of
two
are
snumbers
and
may
possess
more
than
one
representation
as
a
sum
of
consecutive
numbers,
depending
on
their
odd
divisors.
The
term
“snumbers”
is
informal
and
not
part
of
standard
mathematical
nomenclature,
but
it
provides
a
convenient
label
for
this
representational
property.