λ
Sigma Notebook

390,816

25 × 32 × 23 × 59
Abundant Even Composite

390,816 is even and not a perfect square. Its factorization is 2^5 × 3^2 × 23 × 59 and its 72 divisors sum to 1,179,360.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 23 × 59
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 1,179,360
Proper Divisor Sum 788,544
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #390809 ← → #390821

Radix Representation

Decimal 390816
Binary 1011111011010100000 (19 bits)
Octal 0o1373240
Hexadecimal 0x5F6A0

Divisor Catalog (60 of 72)

1 2 3 4 6 8 9 12 16 18 23 24 32 36 46 48 59 69 72 92 96 118 138 144 177 184 207 236 276 288 354 368 414 472 531 552 708 736 828 944 1,062 1,104 1,357 1,416 1,656 1,888 2,124 2,208 2,714 2,832 3,312 4,071 4,248 5,428 5,664 6,624 8,142 8,496 10,856 12,213

Collatz Trajectory (161 steps to reach 1)

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

390,816 195,408 97,704 48,852 24,426 12,213 36,640 18,320 9,160 4,580 2,290 1,145 3,436 1,718 859 2,578 1,289 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532 3,266 1,633 4,900 2,450 1,225 3,676 1,838 919 2,758 1,379 4,138 2,069 6,208 3,104 1,552 776 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71

More profiles

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