λ
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Atlas › Integer Profiles › Node 30,007,516

30,007,516

22 × 7 × 112 × 17 × 521
Abundant Even Composite

30,007,516 factors as 2^2 × 7 × 11^2 × 17 × 521. Its 72 positive divisors give a proper-divisor sum of 39,973,892, so this integer is abundant. The Collatz stopping time is 224 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 11^2 × 17 × 521
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 69,981,408
Proper Divisor Sum 39,973,892
Digit Sum / Digital Root 22 (Root: 4)
Adjacent Primes #30007501 ← → #30007553

Radix Representation

Decimal 30007516
Binary 1110010011110000011011100 (25 bits)
Octal 0o162360334
Hexadecimal 0x1C9E0DC

Divisor Catalog (60 of 72)

1 2 4 7 11 14 17 22 28 34 44 68 77 119 121 154 187 238 242 308 374 476 484 521 748 847 1,042 1,309 1,694 2,057 2,084 2,618 3,388 3,647 4,114 5,236 5,731 7,294 8,228 8,857 11,462 14,399 14,588 17,714 22,924 28,798 35,428 40,117 57,596 61,999 63,041 80,234 97,427 123,998 126,082 160,468 194,854 247,996 252,164 389,708

Collatz Trajectory (224 steps to reach 1)

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

30,007,516 15,003,758 7,501,879 22,505,638 11,252,819 33,758,458 16,879,229 50,637,688 25,318,844 12,659,422 6,329,711 18,989,134 9,494,567 28,483,702 14,241,851 42,725,554 21,362,777 64,088,332 32,044,166 16,022,083 48,066,250 24,033,125 72,099,376 36,049,688 18,024,844 9,012,422 4,506,211 13,518,634 6,759,317 20,277,952 10,138,976 5,069,488 2,534,744 1,267,372 633,686 316,843 950,530 475,265 1,425,796 712,898 356,449 1,069,348 534,674 267,337 802,012 401,006 200,503 601,510 300,755 902,266 451,133 1,353,400 676,700 338,350 169,175 507,526 253,763 761,290 380,645 1,141,936

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