λ
Harmonic Matrix

3,159,024

24 × 3 × 11 × 31 × 193
Abundant Even Composite

3,159,024 has digital root 6. The neighboring primes are 3159017 and 3159029; its proper-divisor sum differs from the starting integer by 2,919,456.

Prime Factor Structure

Factorization String 2^4 × 3 × 11 × 31 × 193
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 9,237,504
Proper Divisor Sum 6,078,480
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #3159017 ← → #3159029

Radix Representation

Decimal 3159024
Binary 1100000011001111110000 (22 bits)
Octal 0o14031760
Hexadecimal 0x3033F0

Divisor Catalog (60 of 80)

1 2 3 4 6 8 11 12 16 22 24 31 33 44 48 62 66 88 93 124 132 176 186 193 248 264 341 372 386 496 528 579 682 744 772 1,023 1,158 1,364 1,488 1,544 2,046 2,123 2,316 2,728 3,088 4,092 4,246 4,632 5,456 5,983 6,369 8,184 8,492 9,264 11,966 12,738 16,368 16,984 17,949 23,932

Collatz Trajectory (195 steps to reach 1)

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

3,159,024 1,579,512 789,756 394,878 197,439 592,318 296,159 888,478 444,239 1,332,718 666,359 1,999,078 999,539 2,998,618 1,499,309 4,497,928 2,248,964 1,124,482 562,241 1,686,724 843,362 421,681 1,265,044 632,522 316,261 948,784 474,392 237,196 118,598 59,299 177,898 88,949 266,848 133,424 66,712 33,356 16,678 8,339 25,018 12,509 37,528 18,764 9,382 4,691 14,074 7,037 21,112 10,556 5,278 2,639 7,918 3,959 11,878 5,939 17,818 8,909 26,728 13,364 6,682 3,341

More profiles

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