λ
Harmonic Matrix

430,727

11 × 39157
Deficient Odd Composite

430,727 has digital root 5. The neighboring primes are 430723 and 430739; its proper-divisor sum differs from the starting integer by -391,558.

Prime Factor Structure

Factorization String 11 × 39157
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 469,896
Proper Divisor Sum 39,169
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #430723 ← → #430739

Radix Representation

Decimal 430727
Binary 1101001001010000111 (19 bits)
Octal 0o1511207
Hexadecimal 0x69287

Divisor Catalog (4)

1 11 39,157 430,727

Collatz Trajectory (55 steps to reach 1)

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

430,727 1,292,182 646,091 1,938,274 969,137 2,907,412 1,453,706 726,853 2,180,560 1,090,280 545,140 272,570 136,285 408,856 204,428 102,214 51,107 153,322 76,661 229,984 114,992 57,496 28,748 14,374 7,187 21,562 10,781 32,344 16,172 8,086 4,043 12,130 6,065 18,196 9,098 4,549 13,648 6,824 3,412 1,706 853 2,560 1,280 640 320 160 80 40 20 10 5 16 8 4 2 1

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