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Atlas › Integer Profiles › Node 1,527,760

1,527,760

24 × 5 × 132 × 113
Abundant Even Composite

1,527,760 factors as 2^4 × 5 × 13^2 × 113. Its 60 positive divisors give a proper-divisor sum of 2,352,572, so this integer is abundant. The Collatz stopping time is 106 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 13^2 × 113
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 3,880,332
Proper Divisor Sum 2,352,572
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #1527737 ← → #1527761

Radix Representation

Decimal 1527760
Binary 101110100111111010000 (21 bits)
Octal 0o5647720
Hexadecimal 0x174FD0

Divisor Catalog (60)

1 2 4 5 8 10 13 16 20 26 40 52 65 80 104 113 130 169 208 226 260 338 452 520 565 676 845 904 1,040 1,130 1,352 1,469 1,690 1,808 2,260 2,704 2,938 3,380 4,520 5,876 6,760 7,345 9,040 11,752 13,520 14,690 19,097 23,504 29,380 38,194 58,760 76,388 95,485 117,520 152,776 190,970 305,552 381,940 763,880 1,527,760

Collatz Trajectory (106 steps to reach 1)

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

1,527,760 763,880 381,940 190,970 95,485 286,456 143,228 71,614 35,807 107,422 53,711 161,134 80,567 241,702 120,851 362,554 181,277 543,832 271,916 135,958 67,979 203,938 101,969 305,908 152,954 76,477 229,432 114,716 57,358 28,679 86,038 43,019 129,058 64,529 193,588 96,794 48,397 145,192 72,596 36,298 18,149 54,448 27,224 13,612 6,806 3,403 10,210 5,105 15,316 7,658 3,829 11,488 5,744 2,872 1,436 718 359 1,078 539 1,618

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