λ
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Atlas › Integer Profiles › Node 34,061,800

34,061,800

23 × 52 × 73 × 2333
Abundant Even Composite

34,061,800 factors as 2^3 × 5^2 × 73 × 2333. Its 48 positive divisors give a proper-divisor sum of 46,251,140, so this integer is abundant. The Collatz stopping time is 232 steps.

Prime Factor Structure

Factorization String 2^3 × 5^2 × 73 × 2333
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 80,312,940
Proper Divisor Sum 46,251,140
Digit Sum / Digital Root 22 (Root: 4)
Adjacent Primes #34061779 ← → #34061801

Radix Representation

Decimal 34061800
Binary 10000001111011110111101000 (26 bits)
Octal 0o201736750
Hexadecimal 0x207BDE8

Divisor Catalog (48)

1 2 4 5 8 10 20 25 40 50 73 100 146 200 292 365 584 730 1,460 1,825 2,333 2,920 3,650 4,666 7,300 9,332 11,665 14,600 18,664 23,330 46,660 58,325 93,320 116,650 170,309 233,300 340,618 466,600 681,236 851,545 1,362,472 1,703,090 3,406,180 4,257,725 6,812,360 8,515,450 17,030,900 34,061,800

Collatz Trajectory (232 steps to reach 1)

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

34,061,800 17,030,900 8,515,450 4,257,725 12,773,176 6,386,588 3,193,294 1,596,647 4,789,942 2,394,971 7,184,914 3,592,457 10,777,372 5,388,686 2,694,343 8,083,030 4,041,515 12,124,546 6,062,273 18,186,820 9,093,410 4,546,705 13,640,116 6,820,058 3,410,029 10,230,088 5,115,044 2,557,522 1,278,761 3,836,284 1,918,142 959,071 2,877,214 1,438,607 4,315,822 2,157,911 6,473,734 3,236,867 9,710,602 4,855,301 14,565,904 7,282,952 3,641,476 1,820,738 910,369 2,731,108 1,365,554 682,777 2,048,332 1,024,166 512,083 1,536,250 768,125 2,304,376 1,152,188 576,094 288,047 864,142 432,071 1,296,214

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