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Atlas › Integer Profiles › Node 72,088,654

72,088,654

2 × 112 × 37 × 83 × 97
Deficient Even Composite

72,088,654 factors as 2 × 11^2 × 37 × 83 × 97. Its 48 positive divisors give a proper-divisor sum of 52,724,930, so this integer is deficient. The Collatz stopping time is 259 steps.

Prime Factor Structure

Factorization String 2 × 11^2 × 37 × 83 × 97
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 124,813,584
Proper Divisor Sum 52,724,930
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #72088633 ← → #72088657

Radix Representation

Decimal 72088654
Binary 100010010111111110001001110 (27 bits)
Octal 0o422776116
Hexadecimal 0x44BFC4E

Divisor Catalog (48)

1 2 11 22 37 74 83 97 121 166 194 242 407 814 913 1,067 1,826 2,134 3,071 3,589 4,477 6,142 7,178 8,051 8,954 10,043 11,737 16,102 20,086 23,474 33,781 39,479 67,562 78,958 88,561 177,122 297,887 371,591 434,269 595,774 743,182 868,538 974,171 1,948,342 3,276,757 6,553,514 36,044,327 72,088,654

Collatz Trajectory (259 steps to reach 1)

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

72,088,654 36,044,327 108,132,982 54,066,491 162,199,474 81,099,737 243,299,212 121,649,606 60,824,803 182,474,410 91,237,205 273,711,616 136,855,808 68,427,904 34,213,952 17,106,976 8,553,488 4,276,744 2,138,372 1,069,186 534,593 1,603,780 801,890 400,945 1,202,836 601,418 300,709 902,128 451,064 225,532 112,766 56,383 169,150 84,575 253,726 126,863 380,590 190,295 570,886 285,443 856,330 428,165 1,284,496 642,248 321,124 160,562 80,281 240,844 120,422 60,211 180,634 90,317 270,952 135,476 67,738 33,869 101,608 50,804 25,402 12,701

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