λ
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Atlas › Integer Profiles › Node 77,266,156

77,266,156

22 × 11 × 17 × 53 × 1949
Abundant Even Composite

77,266,156 factors as 2^2 × 11 × 17 × 53 × 1949. Its 48 positive divisors give a proper-divisor sum of 81,947,444, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^2 × 11 × 17 × 53 × 1949
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 159,213,600
Proper Divisor Sum 81,947,444
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #77266153 ← → #77266169

Radix Representation

Decimal 77266156
Binary 100100110101111110011101100 (27 bits)
Octal 0o446576354
Hexadecimal 0x49AFCEC

Divisor Catalog (48)

1 2 4 11 17 22 34 44 53 68 106 187 212 374 583 748 901 1,166 1,802 1,949 2,332 3,604 3,898 7,796 9,911 19,822 21,439 33,133 39,644 42,878 66,266 85,756 103,297 132,532 206,594 364,463 413,188 728,926 1,136,267 1,457,852 1,756,049 2,272,534 3,512,098 4,545,068 7,024,196 19,316,539 38,633,078 77,266,156

Collatz Trajectory (122 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

77,266,156 38,633,078 19,316,539 57,949,618 28,974,809 86,924,428 43,462,214 21,731,107 65,193,322 32,596,661 97,789,984 48,894,992 24,447,496 12,223,748 6,111,874 3,055,937 9,167,812 4,583,906 2,291,953 6,875,860 3,437,930 1,718,965 5,156,896 2,578,448 1,289,224 644,612 322,306 161,153 483,460 241,730 120,865 362,596 181,298 90,649 271,948 135,974 67,987 203,962 101,981 305,944 152,972 76,486 38,243 114,730 57,365 172,096 86,048 43,024 21,512 10,756 5,378 2,689 8,068 4,034 2,017 6,052 3,026 1,513 4,540 2,270

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