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Atlas › Integer Profiles › Node 81,746,964

81,746,964

22 × 32 × 13 × 174673
Abundant Even Composite

81,746,964 factors as 2^2 × 3^2 × 13 × 174673. Its 36 positive divisors give a proper-divisor sum of 140,787,712, so this integer is abundant. The Collatz stopping time is 130 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 13 × 174673
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 222,534,676
Proper Divisor Sum 140,787,712
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #81746963 ← → #81746981

Radix Representation

Decimal 81746964
Binary 100110111110101110000010100 (27 bits)
Octal 0o467656024
Hexadecimal 0x4DF5C14

Divisor Catalog (36)

1 2 3 4 6 9 12 13 18 26 36 39 52 78 117 156 234 468 174,673 349,346 524,019 698,692 1,048,038 1,572,057 2,096,076 2,270,749 3,144,114 4,541,498 6,288,228 6,812,247 9,082,996 13,624,494 20,436,741 27,248,988 40,873,482 81,746,964

Collatz Trajectory (130 steps to reach 1)

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

81,746,964 40,873,482 20,436,741 61,310,224 30,655,112 15,327,556 7,663,778 3,831,889 11,495,668 5,747,834 2,873,917 8,621,752 4,310,876 2,155,438 1,077,719 3,233,158 1,616,579 4,849,738 2,424,869 7,274,608 3,637,304 1,818,652 909,326 454,663 1,363,990 681,995 2,045,986 1,022,993 3,068,980 1,534,490 767,245 2,301,736 1,150,868 575,434 287,717 863,152 431,576 215,788 107,894 53,947 161,842 80,921 242,764 121,382 60,691 182,074 91,037 273,112 136,556 68,278 34,139 102,418 51,209 153,628 76,814 38,407 115,222 57,611 172,834 86,417

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