In Mathematics
126 is a pentagonal pyramidal number, and a decagonal number as well as a pentatope number.
It is an abundant number. It is the fifth Granville number, and the third such not to be a perfect number. Also, it is known to be the smallest Granville number with three distinct prime factors, and perhaps the only such Granville number.
125 and 126 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.
In base 10, is is a Harshad number as well as a Friedman number, since 126 = 6 × 21.
On the standard 3x3 Rubik's Cube, starting from the original set position, the basic algorithm of alternating top rotation- side rotation will return the cube to its original state in 126 moves.
126 is a binomial coefficient:
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