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Atlas › Integer Profiles › Node 78,286,912

78,286,912

26 × 11 × 61 × 1823
Abundant Even Composite

78,286,912 factors as 2^6 × 11 × 61 × 1823. Its 56 positive divisors give a proper-divisor sum of 94,059,200, so this integer is abundant. The Collatz stopping time is 117 steps.

Prime Factor Structure

Factorization String 2^6 × 11 × 61 × 1823
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 172,346,112
Proper Divisor Sum 94,059,200
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #78286909 ← → #78286927

Radix Representation

Decimal 78286912
Binary 100101010101001000001000000 (27 bits)
Octal 0o452510100
Hexadecimal 0x4AA9040

Divisor Catalog (56)

1 2 4 8 11 16 22 32 44 61 64 88 122 176 244 352 488 671 704 976 1,342 1,823 1,952 2,684 3,646 3,904 5,368 7,292 10,736 14,584 20,053 21,472 29,168 40,106 42,944 58,336 80,212 111,203 116,672 160,424 222,406 320,848 444,812 641,696 889,624 1,223,233 1,283,392 1,779,248 2,446,466 3,558,496 4,892,932 7,116,992 9,785,864 19,571,728 39,143,456 78,286,912

Collatz Trajectory (117 steps to reach 1)

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

78,286,912 39,143,456 19,571,728 9,785,864 4,892,932 2,446,466 1,223,233 3,669,700 1,834,850 917,425 2,752,276 1,376,138 688,069 2,064,208 1,032,104 516,052 258,026 129,013 387,040 193,520 96,760 48,380 24,190 12,095 36,286 18,143 54,430 27,215 81,646 40,823 122,470 61,235 183,706 91,853 275,560 137,780 68,890 34,445 103,336 51,668 25,834 12,917 38,752 19,376 9,688 4,844 2,422 1,211 3,634 1,817 5,452 2,726 1,363 4,090 2,045 6,136 3,068 1,534 767 2,302

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