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Atlas › Integer Profiles › Node 742,220

742,220

22 × 5 × 17 × 37 × 59
Abundant Even Composite

742,220 factors as 2^2 × 5 × 17 × 37 × 59. Its 48 positive divisors give a proper-divisor sum of 981,460, so this integer is abundant. The Collatz stopping time is 118 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 17 × 37 × 59
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,723,680
Proper Divisor Sum 981,460
Digit Sum / Digital Root 17 (Root: 8)
Adjacent Primes #742219 ← → #742229

Radix Representation

Decimal 742220
Binary 10110101001101001100 (20 bits)
Octal 0o2651514
Hexadecimal 0xB534C

Divisor Catalog (48)

1 2 4 5 10 17 20 34 37 59 68 74 85 118 148 170 185 236 295 340 370 590 629 740 1,003 1,180 1,258 2,006 2,183 2,516 3,145 4,012 4,366 5,015 6,290 8,732 10,030 10,915 12,580 20,060 21,830 37,111 43,660 74,222 148,444 185,555 371,110 742,220

Collatz Trajectory (118 steps to reach 1)

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

742,220 371,110 185,555 556,666 278,333 835,000 417,500 208,750 104,375 313,126 156,563 469,690 234,845 704,536 352,268 176,134 88,067 264,202 132,101 396,304 198,152 99,076 49,538 24,769 74,308 37,154 18,577 55,732 27,866 13,933 41,800 20,900 10,450 5,225 15,676 7,838 3,919 11,758 5,879 17,638 8,819 26,458 13,229 39,688 19,844 9,922 4,961 14,884 7,442 3,721 11,164 5,582 2,791 8,374 4,187 12,562 6,281 18,844 9,422 4,711

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