λ
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Atlas › Integer Profiles › Node 10,218,670

10,218,670

2 × 5 × 7 × 11 × 23 × 577
Abundant Even Composite

10,218,670 factors as 2 × 5 × 7 × 11 × 23 × 577. Its 64 positive divisors give a proper-divisor sum of 13,752,146, so this integer is abundant. The Collatz stopping time is 127 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 11 × 23 × 577
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 23,970,816
Proper Divisor Sum 13,752,146
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #10218653 ← → #10218679

Radix Representation

Decimal 10218670
Binary 100110111110110010101110 (24 bits)
Octal 0o46766256
Hexadecimal 0x9BECAE

Divisor Catalog (60 of 64)

1 2 5 7 10 11 14 22 23 35 46 55 70 77 110 115 154 161 230 253 322 385 506 577 770 805 1,154 1,265 1,610 1,771 2,530 2,885 3,542 4,039 5,770 6,347 8,078 8,855 12,694 13,271 17,710 20,195 26,542 31,735 40,390 44,429 63,470 66,355 88,858 92,897 132,710 145,981 185,794 222,145 291,962 444,290 464,485 729,905 928,970 1,021,867

Collatz Trajectory (127 steps to reach 1)

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

10,218,670 5,109,335 15,328,006 7,664,003 22,992,010 11,496,005 34,488,016 17,244,008 8,622,004 4,311,002 2,155,501 6,466,504 3,233,252 1,616,626 808,313 2,424,940 1,212,470 606,235 1,818,706 909,353 2,728,060 1,364,030 682,015 2,046,046 1,023,023 3,069,070 1,534,535 4,603,606 2,301,803 6,905,410 3,452,705 10,358,116 5,179,058 2,589,529 7,768,588 3,884,294 1,942,147 5,826,442 2,913,221 8,739,664 4,369,832 2,184,916 1,092,458 546,229 1,638,688 819,344 409,672 204,836 102,418 51,209 153,628 76,814 38,407 115,222 57,611 172,834 86,417 259,252 129,626 64,813

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