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Atlas › Integer Profiles › Node 20,109,040

20,109,040

24 × 5 × 7 × 149 × 241
Abundant Even Composite

20,109,040 factors as 2^4 × 5 × 7 × 149 × 241. Its 80 positive divisors give a proper-divisor sum of 33,905,360, so this integer is abundant. The Collatz stopping time is 239 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 149 × 241
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 54,014,400
Proper Divisor Sum 33,905,360
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #20109017 ← → #20109041

Radix Representation

Decimal 20109040
Binary 1001100101101011011110000 (25 bits)
Octal 0o114553360
Hexadecimal 0x132D6F0

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 149 241 280 298 482 560 596 745 964 1,043 1,192 1,205 1,490 1,687 1,928 2,086 2,384 2,410 2,980 3,374 3,856 4,172 4,820 5,215 5,960 6,748 8,344 8,435 9,640 10,430 11,920 13,496 16,688 16,870 19,280 20,860 26,992 33,740 35,909 41,720 67,480 71,818

Collatz Trajectory (239 steps to reach 1)

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

20,109,040 10,054,520 5,027,260 2,513,630 1,256,815 3,770,446 1,885,223 5,655,670 2,827,835 8,483,506 4,241,753 12,725,260 6,362,630 3,181,315 9,543,946 4,771,973 14,315,920 7,157,960 3,578,980 1,789,490 894,745 2,684,236 1,342,118 671,059 2,013,178 1,006,589 3,019,768 1,509,884 754,942 377,471 1,132,414 566,207 1,698,622 849,311 2,547,934 1,273,967 3,821,902 1,910,951 5,732,854 2,866,427 8,599,282 4,299,641 12,898,924 6,449,462 3,224,731 9,674,194 4,837,097 14,511,292 7,255,646 3,627,823 10,883,470 5,441,735 16,325,206 8,162,603 24,487,810 12,243,905 36,731,716 18,365,858 9,182,929 27,548,788

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