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Atlas › Integer Profiles › Node 9,727,164

9,727,164

22 × 32 × 19 × 14221
Abundant Even Composite

9,727,164 factors as 2^2 × 3^2 × 19 × 14221. Its 36 positive divisors give a proper-divisor sum of 16,156,876, so this integer is abundant. The Collatz stopping time is 194 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 19 × 14221
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 25,884,040
Proper Divisor Sum 16,156,876
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #9727163 ← → #9727169

Radix Representation

Decimal 9727164
Binary 100101000110110010111100 (24 bits)
Octal 0o45066274
Hexadecimal 0x946CBC

Divisor Catalog (36)

1 2 3 4 6 9 12 18 19 36 38 57 76 114 171 228 342 684 14,221 28,442 42,663 56,884 85,326 127,989 170,652 255,978 270,199 511,956 540,398 810,597 1,080,796 1,621,194 2,431,791 3,242,388 4,863,582 9,727,164

Collatz Trajectory (194 steps to reach 1)

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

9,727,164 4,863,582 2,431,791 7,295,374 3,647,687 10,943,062 5,471,531 16,414,594 8,207,297 24,621,892 12,310,946 6,155,473 18,466,420 9,233,210 4,616,605 13,849,816 6,924,908 3,462,454 1,731,227 5,193,682 2,596,841 7,790,524 3,895,262 1,947,631 5,842,894 2,921,447 8,764,342 4,382,171 13,146,514 6,573,257 19,719,772 9,859,886 4,929,943 14,789,830 7,394,915 22,184,746 11,092,373 33,277,120 16,638,560 8,319,280 4,159,640 2,079,820 1,039,910 519,955 1,559,866 779,933 2,339,800 1,169,900 584,950 292,475 877,426 438,713 1,316,140 658,070 329,035 987,106 493,553 1,480,660 740,330 370,165

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