72

Number
$72$ (seventy-two) is:


 * $2^3 \times 3^2$


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


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


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


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


 * The $18$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$:
 * $\map {\sigma_1} {72} = 195$


 * The $21$st Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$, $16$, $18$, $26$, $28$, $36$, $38$, $47$, $48$, $53$, $57$, $62$, $69$:
 * $72 = 69 + 3$


 * 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 $32$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 $40$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.


 * The $42$nd (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$


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

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