λ
Harmonic Matrix

1,533,720

23 × 3 × 5 × 12781
Abundant Even Composite

1,533,720 has digital root 3. The neighboring primes are 1533713 and 1533731; its proper-divisor sum differs from the starting integer by 1,534,080.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 12781
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 4,601,520
Proper Divisor Sum 3,067,800
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #1533713 ← → #1533731

Radix Representation

Decimal 1533720
Binary 101110110011100011000 (21 bits)
Octal 0o5663430
Hexadecimal 0x176718

Divisor Catalog (32)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 12,781 25,562 38,343 51,124 63,905 76,686 102,248 127,810 153,372 191,715 255,620 306,744 383,430 511,240 766,860 1,533,720

Collatz Trajectory (57 steps to reach 1)

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

1,533,720 766,860 383,430 191,715 575,146 287,573 862,720 431,360 215,680 107,840 53,920 26,960 13,480 6,740 3,370 1,685 5,056 2,528 1,264 632 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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