λ
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Atlas › Integer Profiles › Node 9,508,940

9,508,940

22 × 5 × 72 × 31 × 313
Abundant Even Composite

9,508,940 factors as 2^2 × 5 × 7^2 × 31 × 313. Its 72 positive divisors give a proper-divisor sum of 14,545,972, so this integer is abundant. The Collatz stopping time is 176 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7^2 × 31 × 313
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 24,054,912
Proper Divisor Sum 14,545,972
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #9508927 ← → #9508951

Radix Representation

Decimal 9508940
Binary 100100010001100001001100 (24 bits)
Octal 0o44214114
Hexadecimal 0x91184C

Divisor Catalog (60 of 72)

1 2 4 5 7 10 14 20 28 31 35 49 62 70 98 124 140 155 196 217 245 310 313 434 490 620 626 868 980 1,085 1,252 1,519 1,565 2,170 2,191 3,038 3,130 4,340 4,382 6,076 6,260 7,595 8,764 9,703 10,955 15,190 15,337 19,406 21,910 30,380 30,674 38,812 43,820 48,515 61,348 67,921 76,685 97,030 135,842 153,370

Collatz Trajectory (176 steps to reach 1)

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

9,508,940 4,754,470 2,377,235 7,131,706 3,565,853 10,697,560 5,348,780 2,674,390 1,337,195 4,011,586 2,005,793 6,017,380 3,008,690 1,504,345 4,513,036 2,256,518 1,128,259 3,384,778 1,692,389 5,077,168 2,538,584 1,269,292 634,646 317,323 951,970 475,985 1,427,956 713,978 356,989 1,070,968 535,484 267,742 133,871 401,614 200,807 602,422 301,211 903,634 451,817 1,355,452 677,726 338,863 1,016,590 508,295 1,524,886 762,443 2,287,330 1,143,665 3,430,996 1,715,498 857,749 2,573,248 1,286,624 643,312 321,656 160,828 80,414 40,207 120,622 60,311

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