8,220,027

3 × 17² × 19 × 499

For 8,220,027, the 24 positive divisors have a total of 12,280,000. Removing 8,220,027 leaves 4,059,973, which gives the deficient classification.

Prime Factor Structure

Factorization String 3 × 17^2 × 19 × 499

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 12,280,000

Proper Divisor Sum 4,059,973

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #8220013 ← → #8220089

Radix Representation

Decimal	8220027
Binary	11111010110110101111011 (23 bits)
Octal	0o37266573
Hexadecimal	0x7D6D7B

Divisor Catalog (24)

1 3 17 19 51 57 289 323 499 867 969 1,497 5,491 8,483 9,481 16,473 25,449 28,443 144,211 161,177 432,633 483,531 2,740,009 8,220,027

Collatz Trajectory (217 steps to reach 1)

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

8,220,027 24,660,082 12,330,041 36,990,124 18,495,062 9,247,531 27,742,594 13,871,297 41,613,892 20,806,946 10,403,473 31,210,420 15,605,210 7,802,605 23,407,816 11,703,908 5,851,954 2,925,977 8,777,932 4,388,966 2,194,483 6,583,450 3,291,725 9,875,176 4,937,588 2,468,794 1,234,397 3,703,192 1,851,596 925,798 462,899 1,388,698 694,349 2,083,048 1,041,524 520,762 260,381 781,144 390,572 195,286 97,643 292,930 146,465 439,396 219,698 109,849 329,548 164,774 82,387 247,162 123,581 370,744 185,372 92,686 46,343 139,030 69,515 208,546 104,273 312,820

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