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Atlas › Integer Profiles › Node 7,204,520

7,204,520

23 × 5 × 23 × 41 × 191
Abundant Even Composite

7,204,520 factors as 2^3 × 5 × 23 × 41 × 191. Its 64 positive divisors give a proper-divisor sum of 10,213,720, so this integer is abundant. The Collatz stopping time is 116 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 23 × 41 × 191
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 17,418,240
Proper Divisor Sum 10,213,720
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #7204517 ← → #7204523

Radix Representation

Decimal 7204520
Binary 11011011110111010101000 (23 bits)
Octal 0o33367250
Hexadecimal 0x6DEEA8

Divisor Catalog (60 of 64)

1 2 4 5 8 10 20 23 40 41 46 82 92 115 164 184 191 205 230 328 382 410 460 764 820 920 943 955 1,528 1,640 1,886 1,910 3,772 3,820 4,393 4,715 7,544 7,640 7,831 8,786 9,430 15,662 17,572 18,860 21,965 31,324 35,144 37,720 39,155 43,930 62,648 78,310 87,860 156,620 175,720 180,113 313,240 360,226 720,452 900,565

Collatz Trajectory (116 steps to reach 1)

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

7,204,520 3,602,260 1,801,130 900,565 2,701,696 1,350,848 675,424 337,712 168,856 84,428 42,214 21,107 63,322 31,661 94,984 47,492 23,746 11,873 35,620 17,810 8,905 26,716 13,358 6,679 20,038 10,019 30,058 15,029 45,088 22,544 11,272 5,636 2,818 1,409 4,228 2,114 1,057 3,172 1,586 793 2,380 1,190 595 1,786 893 2,680 1,340 670 335 1,006 503 1,510 755 2,266 1,133 3,400 1,700 850 425 1,276

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