λ
Harmonic Matrix

5,497,731

32 × 41 × 47 × 317
Deficient Odd Composite

5,497,731 has digital root 9. The neighboring primes are 5497721 and 5497753; its proper-divisor sum differs from the starting integer by -2,661,318.

Prime Factor Structure

Factorization String 3^2 × 41 × 47 × 317
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 8,334,144
Proper Divisor Sum 2,836,413
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #5497721 ← → #5497753

Radix Representation

Decimal 5497731
Binary 10100111110001110000011 (23 bits)
Octal 0o24761603
Hexadecimal 0x53E383

Divisor Catalog (24)

1 3 9 41 47 123 141 317 369 423 951 1,927 2,853 5,781 12,997 14,899 17,343 38,991 44,697 116,973 134,091 610,859 1,832,577 5,497,731

Collatz Trajectory (263 steps to reach 1)

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

5,497,731 16,493,194 8,246,597 24,739,792 12,369,896 6,184,948 3,092,474 1,546,237 4,638,712 2,319,356 1,159,678 579,839 1,739,518 869,759 2,609,278 1,304,639 3,913,918 1,956,959 5,870,878 2,935,439 8,806,318 4,403,159 13,209,478 6,604,739 19,814,218 9,907,109 29,721,328 14,860,664 7,430,332 3,715,166 1,857,583 5,572,750 2,786,375 8,359,126 4,179,563 12,538,690 6,269,345 18,808,036 9,404,018 4,702,009 14,106,028 7,053,014 3,526,507 10,579,522 5,289,761 15,869,284 7,934,642 3,967,321 11,901,964 5,950,982 2,975,491 8,926,474 4,463,237 13,389,712 6,694,856 3,347,428 1,673,714 836,857 2,510,572 1,255,286

More profiles

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