λ
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Atlas › Integer Profiles › Node 772,092

772,092

22 × 34 × 2383
Abundant Even Composite

772,092 factors as 2^2 × 3^4 × 2383. Its 30 positive divisors give a proper-divisor sum of 1,247,156, so this integer is abundant. The Collatz stopping time is 224 steps.

Prime Factor Structure

Factorization String 2^2 × 3^4 × 2383
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 30
Divisor Sum (σ) 2,019,248
Proper Divisor Sum 1,247,156
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #772091 ← → #772097

Radix Representation

Decimal 772092
Binary 10111100011111111100 (20 bits)
Octal 0o2743774
Hexadecimal 0xBC7FC

Divisor Catalog (30)

1 2 3 4 6 9 12 18 27 36 54 81 108 162 324 2,383 4,766 7,149 9,532 14,298 21,447 28,596 42,894 64,341 85,788 128,682 193,023 257,364 386,046 772,092

Collatz Trajectory (224 steps to reach 1)

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

772,092 386,046 193,023 579,070 289,535 868,606 434,303 1,302,910 651,455 1,954,366 977,183 2,931,550 1,465,775 4,397,326 2,198,663 6,595,990 3,297,995 9,893,986 4,946,993 14,840,980 7,420,490 3,710,245 11,130,736 5,565,368 2,782,684 1,391,342 695,671 2,087,014 1,043,507 3,130,522 1,565,261 4,695,784 2,347,892 1,173,946 586,973 1,760,920 880,460 440,230 220,115 660,346 330,173 990,520 495,260 247,630 123,815 371,446 185,723 557,170 278,585 835,756 417,878 208,939 626,818 313,409 940,228 470,114 235,057 705,172 352,586 176,293

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