65 = 12 + 3 + 4 × 5 + 6 + 7 + 8 + 9
65 = 9 + 8 + 7 + 6 × 5 + 4 + 3 × 2 + 1
65 = 0^6 + 1^9 + 2^1 + 3^7 − 4^8 + 5^0 + 6^3 + 7^2 + 8^4 + 9^5
65 = 1^2 + 8^2 = 4^2 + 7^2
65^2 = 16^2 + 63^2 = 33^2 + 56^2
654 = 14+84+124+324+644
654 = 24+394+444+464+52465 = 9 + 8 + 7 + 6 × 5 + 4 + 3 × 2 + 1
65 = (1 + 1)((1+1)×(1+1+1)) + 1
= 2(2+2+2) + 2/2
= (3 + 3/3)3 + 3/3
= (44 + 4)/4
= 55 + 5 + 5
= 66 − 6/6
= 77 − (77 + 7)/7
= 8 × 8 + 8/8
= 9 × 9 − 9 − 9 + (9 + 9)/9
65 = 55_12 in base 12.
Number of fractions in Farey series of order 14 : 0/1, 1/14, 1/13, 1/12, 1/11, 1/10, 1/9, 1/8, 1/7, 2/13, 1/6, 2/11, 1/5, 3/14, 2/9, 3/13, 1/4, 3/11, 2/7, 3/10, 4/13, 1/3, 5/14, 4/11, 3/8, 5/13, 2/5, 5/12, 3/7, 4/9, 5/11, 6/13, 1/2, 7/13, 6/11, 5/9, 4/7, 7/12, 3/5, 8/13, 5/8, 7/11, 9/14, 2/3, 9/13, 7/10, 5/7, 8/11, 3/4, 10/13, 7/9, 11/14, 4/5, 9/11, 5/6, 11/13, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12, 12/13, 13/14, 1/1
Number that is the sum of 3 positive 5th powers.
a(n) is the product of the first n primes congruent to 1 (mod 4).
Moser-de Bruijn sequence: sums of distinct powers of 4
Numbers k such that (8*10^k + 49)/3 is prime.
Odd number n such that 3^n+1 is a sum of two squares. \( 3^65 + 1 = 10301051460877537453973547267844 \) (10 nonillion 301 octillion 51 septillion 460 sextillion 877 quintillion 537 quadrillion 453 trillion 973 billion 547 million 267 thousand 844)
Magic Square with numbers 1 to 25 and Sum 65
| 10 | 18 | 1 | 14 | 22 |
| 11 | 24 | 7 | 20 | 3 |
| 17 | 5 | 13 | 21 | 9 |
| 23 | 6 | 10 | 2 | 15 |
| 4 | 12 | 25 | 8 | 16 |
Factors: 1, 5, 13, 65
Representations, Binary to Hexadecimal:
1000001_2
2102_3
1001_4
230_5
145_6
122_7
101_8
72_9
5a_11
55_12
50_13
49_14
45_15
41_16
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