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Atlas › Integer Profiles › Node 13,829,976

13,829,976

23 × 32 × 17 × 11299
Abundant Even Composite

13,829,976 factors as 2^3 × 3^2 × 17 × 11299. Its 48 positive divisors give a proper-divisor sum of 25,833,024, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 17 × 11299
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 39,663,000
Proper Divisor Sum 25,833,024
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #13829947 ← → #13829987

Radix Representation

Decimal 13829976
Binary 110100110000011101011000 (24 bits)
Octal 0o64603530
Hexadecimal 0xD30758

Divisor Catalog (48)

1 2 3 4 6 8 9 12 17 18 24 34 36 51 68 72 102 136 153 204 306 408 612 1,224 11,299 22,598 33,897 45,196 67,794 90,392 101,691 135,588 192,083 203,382 271,176 384,166 406,764 576,249 768,332 813,528 1,152,498 1,536,664 1,728,747 2,304,996 3,457,494 4,609,992 6,914,988 13,829,976

Collatz Trajectory (192 steps to reach 1)

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

13,829,976 6,914,988 3,457,494 1,728,747 5,186,242 2,593,121 7,779,364 3,889,682 1,944,841 5,834,524 2,917,262 1,458,631 4,375,894 2,187,947 6,563,842 3,281,921 9,845,764 4,922,882 2,461,441 7,384,324 3,692,162 1,846,081 5,538,244 2,769,122 1,384,561 4,153,684 2,076,842 1,038,421 3,115,264 1,557,632 778,816 389,408 194,704 97,352 48,676 24,338 12,169 36,508 18,254 9,127 27,382 13,691 41,074 20,537 61,612 30,806 15,403 46,210 23,105 69,316 34,658 17,329 51,988 25,994 12,997 38,992 19,496 9,748 4,874 2,437

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