6,540,040

2³ × 5 × 13 × 12577

Starting at 6,540,040, the Collatz iteration reaches 1 after 178 steps. The first transition is 3270020; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 13 × 12577

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 15,848,280

Proper Divisor Sum 9,308,240

Digit Sum / Digital Root 19 (Root: 1)

Adjacent Primes #6540029 ← → #6540067

Radix Representation

Decimal	6540040
Binary	11000111100101100001000 (23 bits)
Octal	0o30745410
Hexadecimal	0x63CB08

Divisor Catalog (32)

1 2 4 5 8 10 13 20 26 40 52 65 104 130 260 520 12,577 25,154 50,308 62,885 100,616 125,770 163,501 251,540 327,002 503,080 654,004 817,505 1,308,008 1,635,010 3,270,020 6,540,040

Collatz Trajectory (178 steps to reach 1)

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

6,540,040 3,270,020 1,635,010 817,505 2,452,516 1,226,258 613,129 1,839,388 919,694 459,847 1,379,542 689,771 2,069,314 1,034,657 3,103,972 1,551,986 775,993 2,327,980 1,163,990 581,995 1,745,986 872,993 2,618,980 1,309,490 654,745 1,964,236 982,118 491,059 1,473,178 736,589 2,209,768 1,104,884 552,442 276,221 828,664 414,332 207,166 103,583 310,750 155,375 466,126 233,063 699,190 349,595 1,048,786 524,393 1,573,180 786,590 393,295 1,179,886 589,943 1,769,830 884,915 2,654,746 1,327,373 3,982,120 1,991,060 995,530 497,765 1,493,296

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