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Atlas › Integer Profiles › Node 2,012,610

2,012,610

2 × 3 × 5 × 73 × 919
Abundant Even Composite

2,012,610 factors as 2 × 3 × 5 × 73 × 919. Its 32 positive divisors give a proper-divisor sum of 2,889,150, so this integer is abundant. The Collatz stopping time is 91 steps.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 73 × 919
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 4,901,760
Proper Divisor Sum 2,889,150
Digit Sum / Digital Root 12 (Root: 3)
Adjacent Primes #2012597 ← → #2012611

Radix Representation

Decimal 2012610
Binary 111101011010111000010 (21 bits)
Octal 0o7532702
Hexadecimal 0x1EB5C2

Divisor Catalog (32)

1 2 3 5 6 10 15 30 73 146 219 365 438 730 919 1,095 1,838 2,190 2,757 4,595 5,514 9,190 13,785 27,570 67,087 134,174 201,261 335,435 402,522 670,870 1,006,305 2,012,610

Collatz Trajectory (91 steps to reach 1)

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

2,012,610 1,006,305 3,018,916 1,509,458 754,729 2,264,188 1,132,094 566,047 1,698,142 849,071 2,547,214 1,273,607 3,820,822 1,910,411 5,731,234 2,865,617 8,596,852 4,298,426 2,149,213 6,447,640 3,223,820 1,611,910 805,955 2,417,866 1,208,933 3,626,800 1,813,400 906,700 453,350 226,675 680,026 340,013 1,020,040 510,020 255,010 127,505 382,516 191,258 95,629 286,888 143,444 71,722 35,861 107,584 53,792 26,896 13,448 6,724 3,362 1,681 5,044 2,522 1,261 3,784 1,892 946 473 1,420 710 355

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