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Numberedisn

Numberedisn is a fictional mathematical construct commonly referenced in puzzle and hobbyist discussions about numeric encodings. It is defined as a simple invariant attached to each positive integer, intended to illustrate how multiple arithmetic features of a number can be combined into a single value.

Under the commonly used variant, Numberedisn(n) is defined as N(n) = s(n) + d(n), where s(n) is the

Examples: For n = 12, s(12) = 3 and d(12) = 6, so N(12) = 9. For n = 7, s(7)

This function is not injective; distinct integers can share the same Numberedisn value (e.g., 12 and 7

Applications and notes: Numberedisn can be used in puzzles and teaching to demonstrate how two simple arithmetic

Related topics include the digit sum function, the divisor-counting function, and additive arithmetic functions.

sum
of
the
decimal
digits
of
n
and
d(n)
is
the
number
of
positive
divisors
of
n.
=
7
and
d(7)
=
2,
so
N(7)
=
9.
both
map
to
9).
As
n
grows,
s(n)
increases
roughly
with
the
number
of
digits,
while
d(n)
varies
irregularly
but
grows
slowly
on
average,
so
N(n)
tends
to
increase
slowly.
statistics
interact,
to
generate
collisions
for
coding
challenges,
or
to
prompt
questions
about
distribution
and
inverse
problems.
There
is
no
formal
standard
definition,
and
the
term
is
not
used
in
mainstream
number
theory
beyond
hobbyist
contexts.