90,506

2 × 13 × 59²

90,506 factors as 2 × 13 × 59^2. Its 12 positive divisors give a proper-divisor sum of 58,216, so this integer is deficient. The Collatz stopping time is 115 steps.

Prime Factor Structure

Factorization String 2 × 13 × 59^2

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 148,722

Proper Divisor Sum 58,216

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #90499 ← → #90511

Radix Representation

Decimal	90506
Binary	10110000110001010 (17 bits)
Octal	0o260612
Hexadecimal	0x1618A

Divisor Catalog (12)

1 2 13 26 59 118 767 1,534 3,481 6,962 45,253 90,506

Collatz Trajectory (115 steps to reach 1)

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

90,506 45,253 135,760 67,880 33,940 16,970 8,485 25,456 12,728 6,364 3,182 1,591 4,774 2,387 7,162 3,581 10,744 5,372 2,686 1,343 4,030 2,015 6,046 3,023 9,070 4,535 13,606 6,803 20,410 10,205 30,616 15,308 7,654 3,827 11,482 5,741 17,224 8,612 4,306 2,153 6,460 3,230 1,615 4,846 2,423 7,270 3,635 10,906 5,453 16,360 8,180 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454

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