λ
Harmonic Matrix

769,591

769591
Deficient Odd Prime

769,591 has digital root 1. The neighboring primes are 769589 and 769597; its proper-divisor sum differs from the starting integer by -769,590.

Prime Factor Structure

Factorization String 769591
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 769,592
Proper Divisor Sum 1
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #769589 ← → #769597

Radix Representation

Decimal 769591
Binary 10111011111000110111 (20 bits)
Octal 0o2737067
Hexadecimal 0xBBE37

Divisor Catalog (2)

Collatz Trajectory (224 steps to reach 1)

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

769,591 2,308,774 1,154,387 3,463,162 1,731,581 5,194,744 2,597,372 1,298,686 649,343 1,948,030 974,015 2,922,046 1,461,023 4,383,070 2,191,535 6,574,606 3,287,303 9,861,910 4,930,955 14,792,866 7,396,433 22,189,300 11,094,650 5,547,325 16,641,976 8,320,988 4,160,494 2,080,247 6,240,742 3,120,371 9,361,114 4,680,557 14,041,672 7,020,836 3,510,418 1,755,209 5,265,628 2,632,814 1,316,407 3,949,222 1,974,611 5,923,834 2,961,917 8,885,752 4,442,876 2,221,438 1,110,719 3,332,158 1,666,079 4,998,238 2,499,119 7,497,358 3,748,679 11,246,038 5,623,019 16,869,058 8,434,529 25,303,588 12,651,794 6,325,897

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