λ
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Atlas › Integer Profiles › Node 8,097,948

8,097,948

22 × 33 × 97 × 773
Abundant Even Composite

8,097,948 factors as 2^2 × 3^3 × 97 × 773. Its 48 positive divisors give a proper-divisor sum of 13,140,612, so this integer is abundant. The Collatz stopping time is 85 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 97 × 773
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,238,560
Proper Divisor Sum 13,140,612
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #8097941 ← → #8097961

Radix Representation

Decimal 8097948
Binary 11110111001000010011100 (23 bits)
Octal 0o36710234
Hexadecimal 0x7B909C

Divisor Catalog (48)

1 2 3 4 6 9 12 18 27 36 54 97 108 194 291 388 582 773 873 1,164 1,546 1,746 2,319 2,619 3,092 3,492 4,638 5,238 6,957 9,276 10,476 13,914 20,871 27,828 41,742 74,981 83,484 149,962 224,943 299,924 449,886 674,829 899,772 1,349,658 2,024,487 2,699,316 4,048,974 8,097,948

Collatz Trajectory (85 steps to reach 1)

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

8,097,948 4,048,974 2,024,487 6,073,462 3,036,731 9,110,194 4,555,097 13,665,292 6,832,646 3,416,323 10,248,970 5,124,485 15,373,456 7,686,728 3,843,364 1,921,682 960,841 2,882,524 1,441,262 720,631 2,161,894 1,080,947 3,242,842 1,621,421 4,864,264 2,432,132 1,216,066 608,033 1,824,100 912,050 456,025 1,368,076 684,038 342,019 1,026,058 513,029 1,539,088 769,544 384,772 192,386 96,193 288,580 144,290 72,145 216,436 108,218 54,109 162,328 81,164 40,582 20,291 60,874 30,437 91,312 45,656 22,828 11,414 5,707 17,122 8,561

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