λ
Harmonic Matrix

1,297,585

5 × 259517
Deficient Odd Composite

1,297,585 has digital root 1. The neighboring primes are 1297573 and 1297601; its proper-divisor sum differs from the starting integer by -1,038,062.

Prime Factor Structure

Factorization String 5 × 259517
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 1,557,108
Proper Divisor Sum 259,523
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #1297573 ← → #1297601

Radix Representation

Decimal 1297585
Binary 100111100110010110001 (21 bits)
Octal 0o4746261
Hexadecimal 0x13CCB1

Divisor Catalog (4)

1 5 259,517 1,297,585

Collatz Trajectory (67 steps to reach 1)

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

1,297,585 3,892,756 1,946,378 973,189 2,919,568 1,459,784 729,892 364,946 182,473 547,420 273,710 136,855 410,566 205,283 615,850 307,925 923,776 461,888 230,944 115,472 57,736 28,868 14,434 7,217 21,652 10,826 5,413 16,240 8,120 4,060 2,030 1,015 3,046 1,523 4,570 2,285 6,856 3,428 1,714 857 2,572 1,286 643 1,930 965 2,896 1,448 724 362 181 544 272 136 68 34 17 52 26 13 40

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