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Atlas › Integer Profiles › Node 77,587,136

77,587,136

26 × 112 × 43 × 233
Abundant Even Composite

Prime Factor Structure

Factorization String 2^6 × 11^2 × 43 × 233
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 84
Divisor Sum (σ) 173,909,736
Proper Divisor Sum 96,322,600
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #77587123 ← → #77587157

Radix Representation

Decimal 77587136
Binary 100100111111110001011000000 (27 bits)
Octal 0o447761300
Hexadecimal 0x49FE2C0

Divisor Catalog (60 of 84)

1 2 4 8 11 16 22 32 43 44 64 86 88 121 172 176 233 242 344 352 466 473 484 688 704 932 946 968 1,376 1,864 1,892 1,936 2,563 2,752 3,728 3,784 3,872 5,126 5,203 7,456 7,568 7,744 10,019 10,252 10,406 14,912 15,136 20,038 20,504 20,812 28,193 30,272 40,076 41,008 41,624 56,386 80,152 82,016 83,248 110,209

Collatz Trajectory (117 steps to reach 1)

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

77,587,136 38,793,568 19,396,784 9,698,392 4,849,196 2,424,598 1,212,299 3,636,898 1,818,449 5,455,348 2,727,674 1,363,837 4,091,512 2,045,756 1,022,878 511,439 1,534,318 767,159 2,301,478 1,150,739 3,452,218 1,726,109 5,178,328 2,589,164 1,294,582 647,291 1,941,874 970,937 2,912,812 1,456,406 728,203 2,184,610 1,092,305 3,276,916 1,638,458 819,229 2,457,688 1,228,844 614,422 307,211 921,634 460,817 1,382,452 691,226 345,613 1,036,840 518,420 259,210 129,605 388,816 194,408 97,204 48,602 24,301 72,904 36,452 18,226 9,113 27,340 13,670

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