λ
Harmonic Matrix

9,624,740

22 × 5 × 151 × 3187
Abundant Even Composite

9,624,740 has digital root 5. The neighboring primes are 9624721 and 9624761; its proper-divisor sum differs from the starting integer by 1,102,712.

Prime Factor Structure

Factorization String 2^2 × 5 × 151 × 3187
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 20,352,192
Proper Divisor Sum 10,727,452
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #9624721 ← → #9624761

Radix Representation

Decimal 9624740
Binary 100100101101110010100100 (24 bits)
Octal 0o44556244
Hexadecimal 0x92DCA4

Divisor Catalog (24)

1 2 4 5 10 20 151 302 604 755 1,510 3,020 3,187 6,374 12,748 15,935 31,870 63,740 481,237 962,474 1,924,948 2,406,185 4,812,370 9,624,740

Collatz Trajectory (145 steps to reach 1)

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

9,624,740 4,812,370 2,406,185 7,218,556 3,609,278 1,804,639 5,413,918 2,706,959 8,120,878 4,060,439 12,181,318 6,090,659 18,271,978 9,135,989 27,407,968 13,703,984 6,851,992 3,425,996 1,712,998 856,499 2,569,498 1,284,749 3,854,248 1,927,124 963,562 481,781 1,445,344 722,672 361,336 180,668 90,334 45,167 135,502 67,751 203,254 101,627 304,882 152,441 457,324 228,662 114,331 342,994 171,497 514,492 257,246 128,623 385,870 192,935 578,806 289,403 868,210 434,105 1,302,316 651,158 325,579 976,738 488,369 1,465,108 732,554 366,277

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