72

Number
$72$ (seventy-two) is:


 * $2^3 \times 3^2$


 * The $12$th powerful number after $1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64$


 * The $16$th semiperfect number after $6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66$:
 * $72 = 12 + 24 + 36$


 * The $18$th highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60$:
 * $\sigma \left({72}\right) = 195$


 * The $1$st element of the $1$st set of $4$ positive integers which form an arithmetic progression which all have the same Euler $\phi$ value:
 * $\phi \left({72}\right) = \phi \left({78}\right) = \phi \left({84}\right) = \phi \left({90}\right) = 24$


 * The product of the number of edges, edges per face and faces of a tetrahedron.
 * $6 \times 4 \times 3$


 * The smallest positive integer whose fifth power can be expressed as the sum of $5$ other fifth powers:
 * $72^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5$


 * The $32$nd integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{72} = 4 \, 722 \, 366 \, 482 \, 869 \, 645 \, 213 \, 696$


 * The $25$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, \ldots$


 * The $40$th positive integer after $2, 3, 4, 7, 8, \ldots, 50, 54, 55, 59, 60, 61, 65, 66, 67$ which cannot be expressed as the sum of distinct pentagonal numbers.


 * There are $17$ positive integers which have an Euler $\phi$ value $72$.

Also see

 * Numbers with Euler Phi Value of 72
 * Product of Number of Edges, Edges per Face and Faces of Tetrahedron
 * Smallest 5th Power equal to Sum of 5 other 5th Powers