λ
Harmonic Matrix
Atlas › Integer Profiles › Node 42,525

42,525

35 × 52 × 7
Abundant Odd Composite

42,525 has digital root 9. The neighboring primes are 42509 and 42533; its proper-divisor sum differs from the starting integer by 5,222.

Prime Factor Structure

Factorization String 3^5 × 5^2 × 7
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 90,272
Proper Divisor Sum 47,747
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #42509 ← → #42533

Radix Representation

Decimal 42525
Binary 1010011000011101 (16 bits)
Octal 0o123035
Hexadecimal 0xA61D

Divisor Catalog (36)

1 3 5 7 9 15 21 25 27 35 45 63 75 81 105 135 175 189 225 243 315 405 525 567 675 945 1,215 1,575 1,701 2,025 2,835 4,725 6,075 8,505 14,175 42,525

Collatz Trajectory (57 steps to reach 1)

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

42,525 127,576 63,788 31,894 15,947 47,842 23,921 71,764 35,882 17,941 53,824 26,912 13,456 6,728 3,364 1,682 841 2,524 1,262 631 1,894 947 2,842 1,421 4,264 2,132 1,066 533 1,600 800 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

More profiles

5,399,732 6,250,423 3,596,011 6,491,695 611,945 2,439,208 3,369,758 9,654,854 1,500,400 637,397 278,982 9,226,666 4,595,236 2,322,185 6,563,994 7,583,108
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