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Atlas › Integer Profiles › Node 27,759,446

27,759,446

2 × 11 × 13 × 312 × 101
Deficient Even Composite

27,759,446 factors as 2 × 11 × 13 × 31^2 × 101. Its 48 positive divisors give a proper-divisor sum of 23,288,698, so this integer is deficient. The Collatz stopping time is 162 steps.

Prime Factor Structure

Factorization String 2 × 11 × 13 × 31^2 × 101
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 51,048,144
Proper Divisor Sum 23,288,698
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #27759421 ← → #27759461

Radix Representation

Decimal 27759446
Binary 1101001111001001101010110 (25 bits)
Octal 0o151711526
Hexadecimal 0x1A79356

Divisor Catalog (48)

1 2 11 13 22 26 31 62 101 143 202 286 341 403 682 806 961 1,111 1,313 1,922 2,222 2,626 3,131 4,433 6,262 8,866 10,571 12,493 14,443 21,142 24,986 28,886 34,441 40,703 68,882 81,406 97,061 137,423 194,122 274,846 447,733 895,466 1,067,671 1,261,793 2,135,342 2,523,586 13,879,723 27,759,446

Collatz Trajectory (162 steps to reach 1)

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

27,759,446 13,879,723 41,639,170 20,819,585 62,458,756 31,229,378 15,614,689 46,844,068 23,422,034 11,711,017 35,133,052 17,566,526 8,783,263 26,349,790 13,174,895 39,524,686 19,762,343 59,287,030 29,643,515 88,930,546 44,465,273 133,395,820 66,697,910 33,348,955 100,046,866 50,023,433 150,070,300 75,035,150 37,517,575 112,552,726 56,276,363 168,829,090 84,414,545 253,243,636 126,621,818 63,310,909 189,932,728 94,966,364 47,483,182 23,741,591 71,224,774 35,612,387 106,837,162 53,418,581 160,255,744 80,127,872 40,063,936 20,031,968 10,015,984 5,007,992 2,503,996 1,251,998 625,999 1,877,998 938,999 2,816,998 1,408,499 4,225,498 2,112,749 6,338,248

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