λ
Harmonic Matrix

7,645,736

23 × 7 × 136531
Abundant Even Composite

7,645,736 has digital root 2. The neighboring primes are 7645709 and 7645739; its proper-divisor sum differs from the starting integer by 1,092,368.

Prime Factor Structure

Factorization String 2^3 × 7 × 136531
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 16,383,840
Proper Divisor Sum 8,738,104
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #7645709 ← → #7645739

Radix Representation

Decimal 7645736
Binary 11101001010101000101000 (23 bits)
Octal 0o35125050
Hexadecimal 0x74AA28

Divisor Catalog (16)

1 2 4 7 8 14 28 56 136,531 273,062 546,124 955,717 1,092,248 1,911,434 3,822,868 7,645,736

Collatz Trajectory (85 steps to reach 1)

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

7,645,736 3,822,868 1,911,434 955,717 2,867,152 1,433,576 716,788 358,394 179,197 537,592 268,796 134,398 67,199 201,598 100,799 302,398 151,199 453,598 226,799 680,398 340,199 1,020,598 510,299 1,530,898 765,449 2,296,348 1,148,174 574,087 1,722,262 861,131 2,583,394 1,291,697 3,875,092 1,937,546 968,773 2,906,320 1,453,160 726,580 363,290 181,645 544,936 272,468 136,234 68,117 204,352 102,176 51,088 25,544 12,772 6,386 3,193 9,580 4,790 2,395 7,186 3,593 10,780 5,390 2,695 8,086

More profiles

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