λ
Harmonic Matrix

5,607,378

2 × 32 × 7 × 191 × 233
Abundant Even Composite

5,607,378 has digital root 9. The neighboring primes are 5607361 and 5607379; its proper-divisor sum differs from the starting integer by 2,802,780.

Prime Factor Structure

Factorization String 2 × 3^2 × 7 × 191 × 233
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 14,017,536
Proper Divisor Sum 8,410,158
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #5607361 ← → #5607379

Radix Representation

Decimal 5607378
Binary 10101011000111111010010 (23 bits)
Octal 0o25307722
Hexadecimal 0x558FD2

Divisor Catalog (48)

1 2 3 6 7 9 14 18 21 42 63 126 191 233 382 466 573 699 1,146 1,337 1,398 1,631 1,719 2,097 2,674 3,262 3,438 4,011 4,194 4,893 8,022 9,786 12,033 14,679 24,066 29,358 44,503 89,006 133,509 267,018 311,521 400,527 623,042 801,054 934,563 1,869,126 2,803,689 5,607,378

Collatz Trajectory (131 steps to reach 1)

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

5,607,378 2,803,689 8,411,068 4,205,534 2,102,767 6,308,302 3,154,151 9,462,454 4,731,227 14,193,682 7,096,841 21,290,524 10,645,262 5,322,631 15,967,894 7,983,947 23,951,842 11,975,921 35,927,764 17,963,882 8,981,941 26,945,824 13,472,912 6,736,456 3,368,228 1,684,114 842,057 2,526,172 1,263,086 631,543 1,894,630 947,315 2,841,946 1,420,973 4,262,920 2,131,460 1,065,730 532,865 1,598,596 799,298 399,649 1,198,948 599,474 299,737 899,212 449,606 224,803 674,410 337,205 1,011,616 505,808 252,904 126,452 63,226 31,613 94,840 47,420 23,710 11,855 35,566

More profiles

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