λ
Harmonic Matrix

5,128,991

7 × 732713
Deficient Odd Composite

5,128,991 has digital root 8. The neighboring primes are 5128987 and 5128999; its proper-divisor sum differs from the starting integer by -4,396,270.

Prime Factor Structure

Factorization String 7 × 732713
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 5,861,712
Proper Divisor Sum 732,721
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #5128987 ← → #5128999

Radix Representation

Decimal 5128991
Binary 10011100100001100011111 (23 bits)
Octal 0o23441437
Hexadecimal 0x4E431F

Divisor Catalog (4)

1 7 732,713 5,128,991

Collatz Trajectory (250 steps to reach 1)

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

5,128,991 15,386,974 7,693,487 23,080,462 11,540,231 34,620,694 17,310,347 51,931,042 25,965,521 77,896,564 38,948,282 19,474,141 58,422,424 29,211,212 14,605,606 7,302,803 21,908,410 10,954,205 32,862,616 16,431,308 8,215,654 4,107,827 12,323,482 6,161,741 18,485,224 9,242,612 4,621,306 2,310,653 6,931,960 3,465,980 1,732,990 866,495 2,599,486 1,299,743 3,899,230 1,949,615 5,848,846 2,924,423 8,773,270 4,386,635 13,159,906 6,579,953 19,739,860 9,869,930 4,934,965 14,804,896 7,402,448 3,701,224 1,850,612 925,306 462,653 1,387,960 693,980 346,990 173,495 520,486 260,243 780,730 390,365 1,171,096

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