Harmonic Matrix

3,713,590

2 × 5 × 371359

3,713,590 has digital root 1. The neighboring primes are 3713587 and 3713617; its proper-divisor sum differs from the starting integer by -742,700.

Prime Factor Structure

Factorization String 2 × 5 × 371359

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 6,684,480

Proper Divisor Sum 2,970,890

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #3713587 ← → #3713617

Radix Representation

Decimal	3713590
Binary	1110001010101000110110 (22 bits)
Octal	0o16125066
Hexadecimal	0x38AA36

Divisor Catalog (8)

1 2 5 10 371,359 742,718 1,856,795 3,713,590

Collatz Trajectory (141 steps to reach 1)

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

3,713,590 1,856,795 5,570,386 2,785,193 8,355,580 4,177,790 2,088,895 6,266,686 3,133,343 9,400,030 4,700,015 14,100,046 7,050,023 21,150,070 10,575,035 31,725,106 15,862,553 47,587,660 23,793,830 11,896,915 35,690,746 17,845,373 53,536,120 26,768,060 13,384,030 6,692,015 20,076,046 10,038,023 30,114,070 15,057,035 45,171,106 22,585,553 67,756,660 33,878,330 16,939,165 50,817,496 25,408,748 12,704,374 6,352,187 19,056,562 9,528,281 28,584,844 14,292,422 7,146,211 21,438,634 10,719,317 32,157,952 16,078,976 8,039,488 4,019,744 2,009,872 1,004,936 502,468 251,234 125,617 376,852 188,426 94,213 282,640 141,320

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