λ
Harmonic Matrix

7,940,464

24 × 7 × 31 × 2287
Abundant Even Composite

7,940,464 has digital root 7. The neighboring primes are 7940447 and 7940467; its proper-divisor sum differs from the starting integer by 2,276,640.

Prime Factor Structure

Factorization String 2^4 × 7 × 31 × 2287
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 18,157,568
Proper Divisor Sum 10,217,104
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #7940447 ← → #7940467

Radix Representation

Decimal 7940464
Binary 11110010010100101110000 (23 bits)
Octal 0o36224560
Hexadecimal 0x792970

Divisor Catalog (40)

1 2 4 7 8 14 16 28 31 56 62 112 124 217 248 434 496 868 1,736 2,287 3,472 4,574 9,148 16,009 18,296 32,018 36,592 64,036 70,897 128,072 141,794 256,144 283,588 496,279 567,176 992,558 1,134,352 1,985,116 3,970,232 7,940,464

Collatz Trajectory (186 steps to reach 1)

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

7,940,464 3,970,232 1,985,116 992,558 496,279 1,488,838 744,419 2,233,258 1,116,629 3,349,888 1,674,944 837,472 418,736 209,368 104,684 52,342 26,171 78,514 39,257 117,772 58,886 29,443 88,330 44,165 132,496 66,248 33,124 16,562 8,281 24,844 12,422 6,211 18,634 9,317 27,952 13,976 6,988 3,494 1,747 5,242 2,621 7,864 3,932 1,966 983 2,950 1,475 4,426 2,213 6,640 3,320 1,660 830 415 1,246 623 1,870 935 2,806 1,403

More profiles

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