λ
Harmonic Matrix

7,262,520

23 × 3 × 5 × 60521
Abundant Even Composite

7,262,520 has digital root 6. The neighboring primes are 7262513 and 7262531; its proper-divisor sum differs from the starting integer by 7,262,880.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 60521
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 21,787,920
Proper Divisor Sum 14,525,400
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #7262513 ← → #7262531

Radix Representation

Decimal 7262520
Binary 11011101101000100111000 (23 bits)
Octal 0o33550470
Hexadecimal 0x6ED138

Divisor Catalog (32)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 60,521 121,042 181,563 242,084 302,605 363,126 484,168 605,210 726,252 907,815 1,210,420 1,452,504 1,815,630 2,420,840 3,631,260 7,262,520

Collatz Trajectory (111 steps to reach 1)

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

7,262,520 3,631,260 1,815,630 907,815 2,723,446 1,361,723 4,085,170 2,042,585 6,127,756 3,063,878 1,531,939 4,595,818 2,297,909 6,893,728 3,446,864 1,723,432 861,716 430,858 215,429 646,288 323,144 161,572 80,786 40,393 121,180 60,590 30,295 90,886 45,443 136,330 68,165 204,496 102,248 51,124 25,562 12,781 38,344 19,172 9,586 4,793 14,380 7,190 3,595 10,786 5,393 16,180 8,090 4,045 12,136 6,068 3,034 1,517 4,552 2,276 1,138 569 1,708 854 427 1,282

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