λ
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Atlas › Integer Profiles › Node 72,007,656

72,007,656

23 × 3 × 72 × 61231
Abundant Even Composite

Prime Factor Structure

Factorization String 2^3 × 3 × 7^2 × 61231
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 209,413,440
Proper Divisor Sum 137,405,784
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #72007643 ← → #72007657

Radix Representation

Decimal 72007656
Binary 100010010101011111111101000 (27 bits)
Octal 0o422537750
Hexadecimal 0x44ABFE8

Divisor Catalog (48)

1 2 3 4 6 7 8 12 14 21 24 28 42 49 56 84 98 147 168 196 294 392 588 1,176 61,231 122,462 183,693 244,924 367,386 428,617 489,848 734,772 857,234 1,285,851 1,469,544 1,714,468 2,571,702 3,000,319 3,428,936 5,143,404 6,000,638 9,000,957 10,286,808 12,001,276 18,001,914 24,002,552 36,003,828 72,007,656

Collatz Trajectory (259 steps to reach 1)

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

72,007,656 36,003,828 18,001,914 9,000,957 27,002,872 13,501,436 6,750,718 3,375,359 10,126,078 5,063,039 15,189,118 7,594,559 22,783,678 11,391,839 34,175,518 17,087,759 51,263,278 25,631,639 76,894,918 38,447,459 115,342,378 57,671,189 173,013,568 86,506,784 43,253,392 21,626,696 10,813,348 5,406,674 2,703,337 8,110,012 4,055,006 2,027,503 6,082,510 3,041,255 9,123,766 4,561,883 13,685,650 6,842,825 20,528,476 10,264,238 5,132,119 15,396,358 7,698,179 23,094,538 11,547,269 34,641,808 17,320,904 8,660,452 4,330,226 2,165,113 6,495,340 3,247,670 1,623,835 4,871,506 2,435,753 7,307,260 3,653,630 1,826,815 5,480,446 2,740,223

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