λ
Harmonic Matrix

5,720,238

2 × 32 × 23 × 41 × 337
Abundant Even Composite

5,720,238 has digital root 9. The neighboring primes are 5720233 and 5720243; its proper-divisor sum differs from the starting integer by 1,846,980.

Prime Factor Structure

Factorization String 2 × 3^2 × 23 × 41 × 337
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 13,287,456
Proper Divisor Sum 7,567,218
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #5720233 ← → #5720243

Radix Representation

Decimal 5720238
Binary 10101110100100010101110 (23 bits)
Octal 0o25644256
Hexadecimal 0x5748AE

Divisor Catalog (48)

1 2 3 6 9 18 23 41 46 69 82 123 138 207 246 337 369 414 674 738 943 1,011 1,886 2,022 2,829 3,033 5,658 6,066 7,751 8,487 13,817 15,502 16,974 23,253 27,634 41,451 46,506 69,759 82,902 124,353 139,518 248,706 317,791 635,582 953,373 1,906,746 2,860,119 5,720,238

Collatz Trajectory (170 steps to reach 1)

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

5,720,238 2,860,119 8,580,358 4,290,179 12,870,538 6,435,269 19,305,808 9,652,904 4,826,452 2,413,226 1,206,613 3,619,840 1,809,920 904,960 452,480 226,240 113,120 56,560 28,280 14,140 7,070 3,535 10,606 5,303 15,910 7,955 23,866 11,933 35,800 17,900 8,950 4,475 13,426 6,713 20,140 10,070 5,035 15,106 7,553 22,660 11,330 5,665 16,996 8,498 4,249 12,748 6,374 3,187 9,562 4,781 14,344 7,172 3,586 1,793 5,380 2,690 1,345 4,036 2,018 1,009

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