λ
Harmonic Matrix

598,563

33 × 7 × 3167
Deficient Odd Composite

598,563 has digital root 9. The neighboring primes are 598541 and 598571; its proper-divisor sum differs from the starting integer by -183,366.

Prime Factor Structure

Factorization String 3^3 × 7 × 3167
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 1,013,760
Proper Divisor Sum 415,197
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #598541 ← → #598571

Radix Representation

Decimal 598563
Binary 10010010001000100011 (20 bits)
Octal 0o2221043
Hexadecimal 0x92223

Divisor Catalog (16)

1 3 7 9 21 27 63 189 3,167 9,501 22,169 28,503 66,507 85,509 199,521 598,563

Collatz Trajectory (115 steps to reach 1)

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

598,563 1,795,690 897,845 2,693,536 1,346,768 673,384 336,692 168,346 84,173 252,520 126,260 63,130 31,565 94,696 47,348 23,674 11,837 35,512 17,756 8,878 4,439 13,318 6,659 19,978 9,989 29,968 14,984 7,492 3,746 1,873 5,620 2,810 1,405 4,216 2,108 1,054 527 1,582 791 2,374 1,187 3,562 1,781 5,344 2,672 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638

More profiles

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