λ
Harmonic Matrix
Atlas › Integer Profiles › Node 2,722,575

2,722,575

3 × 52 × 31 × 1171
Deficient Odd Composite

2,722,575 has digital root 3. The neighboring primes are 2722561 and 2722591; its proper-divisor sum differs from the starting integer by -794,654.

Prime Factor Structure

Factorization String 3 × 5^2 × 31 × 1171
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 4,650,496
Proper Divisor Sum 1,927,921
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #2722561 ← → #2722591

Radix Representation

Decimal 2722575
Binary 1010011000101100001111 (22 bits)
Octal 0o12305417
Hexadecimal 0x298B0F

Divisor Catalog (24)

1 3 5 15 25 31 75 93 155 465 775 1,171 2,325 3,513 5,855 17,565 29,275 36,301 87,825 108,903 181,505 544,515 907,525 2,722,575

Collatz Trajectory (63 steps to reach 1)

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

2,722,575 8,167,726 4,083,863 12,251,590 6,125,795 18,377,386 9,188,693 27,566,080 13,783,040 6,891,520 3,445,760 1,722,880 861,440 430,720 215,360 107,680 53,840 26,920 13,460 6,730 3,365 10,096 5,048 2,524 1,262 631 1,894 947 2,842 1,421 4,264 2,132 1,066 533 1,600 800 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16

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