λ
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Atlas › Integer Profiles › Node 34,178,092

34,178,092

22 × 13 × 17 × 23 × 412
Abundant Even Composite

34,178,092 factors as 2^2 × 13 × 17 × 23 × 41^2. Its 72 positive divisors give a proper-divisor sum of 38,766,836, so this integer is abundant. The Collatz stopping time is 126 steps.

Prime Factor Structure

Factorization String 2^2 × 13 × 17 × 23 × 41^2
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 72,944,928
Proper Divisor Sum 38,766,836
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #34178083 ← → #34178101

Radix Representation

Decimal 34178092
Binary 10000010011000010000101100 (26 bits)
Octal 0o202302054
Hexadecimal 0x209842C

Divisor Catalog (60 of 72)

1 2 4 13 17 23 26 34 41 46 52 68 82 92 164 221 299 391 442 533 598 697 782 884 943 1,066 1,196 1,394 1,564 1,681 1,886 2,132 2,788 3,362 3,772 5,083 6,724 9,061 10,166 12,259 16,031 18,122 20,332 21,853 24,518 28,577 32,062 36,244 38,663 43,706 49,036 57,154 64,124 77,326 87,412 114,308 154,652 208,403 371,501 416,806

Collatz Trajectory (126 steps to reach 1)

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

34,178,092 17,089,046 8,544,523 25,633,570 12,816,785 38,450,356 19,225,178 9,612,589 28,837,768 14,418,884 7,209,442 3,604,721 10,814,164 5,407,082 2,703,541 8,110,624 4,055,312 2,027,656 1,013,828 506,914 253,457 760,372 380,186 190,093 570,280 285,140 142,570 71,285 213,856 106,928 53,464 26,732 13,366 6,683 20,050 10,025 30,076 15,038 7,519 22,558 11,279 33,838 16,919 50,758 25,379 76,138 38,069 114,208 57,104 28,552 14,276 7,138 3,569 10,708 5,354 2,677 8,032 4,016 2,008 1,004

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