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Atlas › Integer Profiles › Node 3,972,220

3,972,220

22 × 5 × 7 × 17 × 1669
Abundant Even Composite

3,972,220 factors as 2^2 × 5 × 7 × 17 × 1669. Its 48 positive divisors give a proper-divisor sum of 6,127,940, so this integer is abundant. The Collatz stopping time is 92 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 17 × 1669
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 10,100,160
Proper Divisor Sum 6,127,940
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #3972193 ← → #3972223

Radix Representation

Decimal 3972220
Binary 1111001001110001111100 (22 bits)
Octal 0o17116174
Hexadecimal 0x3C9C7C

Divisor Catalog (48)

1 2 4 5 7 10 14 17 20 28 34 35 68 70 85 119 140 170 238 340 476 595 1,190 1,669 2,380 3,338 6,676 8,345 11,683 16,690 23,366 28,373 33,380 46,732 56,746 58,415 113,492 116,830 141,865 198,611 233,660 283,730 397,222 567,460 794,444 993,055 1,986,110 3,972,220

Collatz Trajectory (92 steps to reach 1)

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

3,972,220 1,986,110 993,055 2,979,166 1,489,583 4,468,750 2,234,375 6,703,126 3,351,563 10,054,690 5,027,345 15,082,036 7,541,018 3,770,509 11,311,528 5,655,764 2,827,882 1,413,941 4,241,824 2,120,912 1,060,456 530,228 265,114 132,557 397,672 198,836 99,418 49,709 149,128 74,564 37,282 18,641 55,924 27,962 13,981 41,944 20,972 10,486 5,243 15,730 7,865 23,596 11,798 5,899 17,698 8,849 26,548 13,274 6,637 19,912 9,956 4,978 2,489 7,468 3,734 1,867 5,602 2,801 8,404 4,202

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