76 (number)

In mathematics

76 is:

• a composite number; a square-prime, of the form (p2, q) where q is a higher prime. It is the ninth of this general form and the seventh of the form (22.q).

• a Lucas number.

• a telephone or involution number, the number of different ways of connecting 6 points with pairwise connections.

• a nontotient.

• a 14-gonal number.

• a centered pentagonal number.

• an Erdős–Woods number since it is possible to find sequences of 76 consecutive integers such that each inner member shares a factor with either the first or the last member.

• with an aliquot sum of 64; within an aliquot sequence of three composite numbers (76,64,63,41,1,0) to the Prime in the 41-aliquot tree.

• an automorphic number in base 10. It is one of two 2-digit numbers whose square, 5,776, and higher powers, end in the same two digits. The other is .

There are 76 unique compact uniform hyperbolic honeycombs in the third dimension that are generated from Wythoff constructions.

References

References

1. "Sloane's A000032 : Lucas numbers". OEIS Foundation.
2. "Sloane's A000085 : Involution numbers". OEIS Foundation.
3. "Sloane's A005277 : Nontotients". OEIS Foundation.
4. "Sloane's A051866 : 14-gonal numbers". OEIS Foundation.
5. "Sloane's A005891 : Centered pentagonal numbers". OEIS Foundation.
6. "Sloane's A059756 : Erdős-Woods numbers". OEIS Foundation.
7. "Sloane's A003226 : Automorphic numbers". OEIS Foundation.