λ
Harmonic Matrix

770,101

770101
Deficient Odd Prime

770,101 has digital root 7. The neighboring primes are 770069 and 770111; its proper-divisor sum differs from the starting integer by -770,100.

Prime Factor Structure

Factorization String 770101
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 770,102
Proper Divisor Sum 1
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #770069 ← → #770111

Radix Representation

Decimal 770101
Binary 10111100000000110101 (20 bits)
Octal 0o2740065
Hexadecimal 0xBC035

Divisor Catalog (2)

1 770,101

Collatz Trajectory (74 steps to reach 1)

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

770,101 2,310,304 1,155,152 577,576 288,788 144,394 72,197 216,592 108,296 54,148 27,074 13,537 40,612 20,306 10,153 30,460 15,230 7,615 22,846 11,423 34,270 17,135 51,406 25,703 77,110 38,555 115,666 57,833 173,500 86,750 43,375 130,126 65,063 195,190 97,595 292,786 146,393 439,180 219,590 109,795 329,386 164,693 494,080 247,040 123,520 61,760 30,880 15,440 7,720 3,860 1,930 965 2,896 1,448 724 362 181 544 272 136

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