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Atlas › Integer Profiles › Node 2,027,960

2,027,960

23 × 5 × 112 × 419
Abundant Even Composite

2,027,960 factors as 2^3 × 5 × 11^2 × 419. Its 48 positive divisors give a proper-divisor sum of 2,999,440, so this integer is abundant. The Collatz stopping time is 184 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 11^2 × 419
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 5,027,400
Proper Divisor Sum 2,999,440
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #2027959 ← → #2028017

Radix Representation

Decimal 2027960
Binary 111101111000110111000 (21 bits)
Octal 0o7570670
Hexadecimal 0x1EF1B8

Divisor Catalog (48)

1 2 4 5 8 10 11 20 22 40 44 55 88 110 121 220 242 419 440 484 605 838 968 1,210 1,676 2,095 2,420 3,352 4,190 4,609 4,840 8,380 9,218 16,760 18,436 23,045 36,872 46,090 50,699 92,180 101,398 184,360 202,796 253,495 405,592 506,990 1,013,980 2,027,960

Collatz Trajectory (184 steps to reach 1)

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

2,027,960 1,013,980 506,990 253,495 760,486 380,243 1,140,730 570,365 1,711,096 855,548 427,774 213,887 641,662 320,831 962,494 481,247 1,443,742 721,871 2,165,614 1,082,807 3,248,422 1,624,211 4,872,634 2,436,317 7,308,952 3,654,476 1,827,238 913,619 2,740,858 1,370,429 4,111,288 2,055,644 1,027,822 513,911 1,541,734 770,867 2,312,602 1,156,301 3,468,904 1,734,452 867,226 433,613 1,300,840 650,420 325,210 162,605 487,816 243,908 121,954 60,977 182,932 91,466 45,733 137,200 68,600 34,300 17,150 8,575 25,726 12,863

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