λ
Harmonic Matrix

1,011,010

2 × 5 × 7 × 11 × 13 × 101
Abundant Even Composite

1,011,010 has digital root 4. The neighboring primes are 1011001 and 1011013; its proper-divisor sum differs from the starting integer by 445,564.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 11 × 13 × 101
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 2,467,584
Proper Divisor Sum 1,456,574
Digit Sum / Digital Root 4 (Root: 4)
Adjacent Primes #1011001 ← → #1011013

Radix Representation

Decimal 1011010
Binary 11110110110101000010 (20 bits)
Octal 0o3666502
Hexadecimal 0xF6D42

Divisor Catalog (60 of 64)

1 2 5 7 10 11 13 14 22 26 35 55 65 70 77 91 101 110 130 143 154 182 202 286 385 455 505 707 715 770 910 1,001 1,010 1,111 1,313 1,414 1,430 2,002 2,222 2,626 3,535 5,005 5,555 6,565 7,070 7,777 9,191 10,010 11,110 13,130 14,443 15,554 18,382 28,886 38,885 45,955 72,215 77,770 91,910 101,101

Collatz Trajectory (82 steps to reach 1)

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

1,011,010 505,505 1,516,516 758,258 379,129 1,137,388 568,694 284,347 853,042 426,521 1,279,564 639,782 319,891 959,674 479,837 1,439,512 719,756 359,878 179,939 539,818 269,909 809,728 404,864 202,432 101,216 50,608 25,304 12,652 6,326 3,163 9,490 4,745 14,236 7,118 3,559 10,678 5,339 16,018 8,009 24,028 12,014 6,007 18,022 9,011 27,034 13,517 40,552 20,276 10,138 5,069 15,208 7,604 3,802 1,901 5,704 2,852 1,426 713 2,140 1,070

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