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Atlas › Integer Profiles › Node 35,201,768

35,201,768

23 × 7 × 73 × 79 × 109
Abundant Even Composite

35,201,768 factors as 2^3 × 7 × 73 × 79 × 109. Its 64 positive divisors give a proper-divisor sum of 42,942,232, so this integer is abundant. The Collatz stopping time is 95 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 73 × 79 × 109
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 78,144,000
Proper Divisor Sum 42,942,232
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #35201743 ← → #35201773

Radix Representation

Decimal 35201768
Binary 10000110010010001011101000 (26 bits)
Octal 0o206221350
Hexadecimal 0x21922E8

Divisor Catalog (60 of 64)

1 2 4 7 8 14 28 56 73 79 109 146 158 218 292 316 436 511 553 584 632 763 872 1,022 1,106 1,526 2,044 2,212 3,052 4,088 4,424 5,767 6,104 7,957 8,611 11,534 15,914 17,222 23,068 31,828 34,444 40,369 46,136 55,699 60,277 63,656 68,888 80,738 111,398 120,554 161,476 222,796 241,108 322,952 445,592 482,216 628,603 1,257,206 2,514,412 4,400,221

Collatz Trajectory (95 steps to reach 1)

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

35,201,768 17,600,884 8,800,442 4,400,221 13,200,664 6,600,332 3,300,166 1,650,083 4,950,250 2,475,125 7,425,376 3,712,688 1,856,344 928,172 464,086 232,043 696,130 348,065 1,044,196 522,098 261,049 783,148 391,574 195,787 587,362 293,681 881,044 440,522 220,261 660,784 330,392 165,196 82,598 41,299 123,898 61,949 185,848 92,924 46,462 23,231 69,694 34,847 104,542 52,271 156,814 78,407 235,222 117,611 352,834 176,417 529,252 264,626 132,313 396,940 198,470 99,235 297,706 148,853 446,560 223,280

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