λ
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Atlas › Integer Profiles › Node 2,478,216

2,478,216

23 × 3 × 133 × 47
Abundant Even Composite

Starting at 2,478,216, the Collatz iteration reaches 1 after 68 steps. The first transition is 1239108; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 13^3 × 47
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 6,854,400
Proper Divisor Sum 4,376,184
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #2478211 ← → #2478221

Radix Representation

Decimal 2478216
Binary 1001011101000010001000 (22 bits)
Octal 0o11350210
Hexadecimal 0x25D088

Divisor Catalog (60 of 64)

1 2 3 4 6 8 12 13 24 26 39 47 52 78 94 104 141 156 169 188 282 312 338 376 507 564 611 676 1,014 1,128 1,222 1,352 1,833 2,028 2,197 2,444 3,666 4,056 4,394 4,888 6,591 7,332 7,943 8,788 13,182 14,664 15,886 17,576 23,829 26,364 31,772 47,658 52,728 63,544 95,316 103,259 190,632 206,518 309,777 413,036

Collatz Trajectory (68 steps to reach 1)

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

2,478,216 1,239,108 619,554 309,777 929,332 464,666 232,333 697,000 348,500 174,250 87,125 261,376 130,688 65,344 32,672 16,336 8,168 4,084 2,042 1,021 3,064 1,532 766 383 1,150 575 1,726 863 2,590 1,295 3,886 1,943 5,830 2,915 8,746 4,373 13,120 6,560 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13

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