1,500,400

2⁴ × 5² × 11² × 31

Starting at 1,500,400, the Collatz iteration reaches 1 after 88 steps. The first transition is 750200; the starting value is even with 90 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 11^2 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 90

Divisor Sum (σ) 4,090,016

Proper Divisor Sum 2,589,616

Digit Sum / Digital Root 10 (Root: 1)

Adjacent Primes #1500397 ← → #1500407

Radix Representation

Decimal	1500400
Binary	101101110010011110000 (21 bits)
Octal	0o5562360
Hexadecimal	0x16E4F0

Divisor Catalog (60 of 90)

1 2 4 5 8 10 11 16 20 22 25 31 40 44 50 55 62 80 88 100 110 121 124 155 176 200 220 242 248 275 310 341 400 440 484 496 550 605 620 682 775 880 968 1,100 1,210 1,240 1,364 1,550 1,705 1,936 2,200 2,420 2,480 2,728 3,025 3,100 3,410 3,751 4,400 4,840

Collatz Trajectory (88 steps to reach 1)

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

1,500,400 750,200 375,100 187,550 93,775 281,326 140,663 421,990 210,995 632,986 316,493 949,480 474,740 237,370 118,685 356,056 178,028 89,014 44,507 133,522 66,761 200,284 100,142 50,071 150,214 75,107 225,322 112,661 337,984 168,992 84,496 42,248 21,124 10,562 5,281 15,844 7,922 3,961 11,884 5,942 2,971 8,914 4,457 13,372 6,686 3,343 10,030 5,015 15,046 7,523 22,570 11,285 33,856 16,928 8,464 4,232 2,116 1,058 529 1,588

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