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124 (number)

From Wikipedia, the free encyclopedia
Natural number
← 123124 125 →
Cardinalone hundred twenty-four
Ordinal124th
(one hundred twenty-fourth)
Factorization22 × 31
Divisors1, 2, 4, 31, 62, 124
Greek numeralΡΚΔ´
Roman numeralCXXIV,cxxiv
Binary11111002
Ternary111213
Senary3246
Octal1748
DuodecimalA412
Hexadecimal7C16

124 (one hundred [and] twenty-four) is thenatural number following123 and preceding125.

In mathematics

[edit]
124magnetic balls arranged into the shape of astella octangula

124 is anuntouchable number, meaning that it is not the sum of proper divisors of any positive number.[1]

It is astella octangula number, the number of spheres packed in the shape of astellated octahedron.[2] It is also anicosahedral number.[3]

There are 124 different polygons of length 12 formed by edges of theinteger lattice, counting two polygons as the same only when one is a translated copy of the other.[4]

124 is a perfectly partitioned number, meaning that it divides thenumber of partitions of 124. It is the first number to do so after 1, 2, and 3.[5]

References

[edit]
  1. ^Sloane, N. J. A. (ed.)."Sequence A005114 (Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A007588 (Stella octangula numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A006564 (Icosahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A002931 (Number of self-avoiding polygons of length 2n on square lattice (not allowing rotations))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A051177 (Perfectly partitioned numbers: numbers k that divide the number of partitions p(k))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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