λ
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Atlas › Integer Profiles › Node 9,707,775

9,707,775

3 × 52 × 7 × 11 × 412
Abundant Odd Composite

9,707,775 factors as 3 × 5^2 × 7 × 11 × 41^2. Its 72 positive divisors give a proper-divisor sum of 10,802,817, so this integer is abundant. The Collatz stopping time is 119 steps.

Prime Factor Structure

Factorization String 3 × 5^2 × 7 × 11 × 41^2
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 20,510,592
Proper Divisor Sum 10,802,817
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #9707773 ← → #9707783

Radix Representation

Decimal 9707775
Binary 100101000010000011111111 (24 bits)
Octal 0o45020377
Hexadecimal 0x9420FF

Divisor Catalog (60 of 72)

1 3 5 7 11 15 21 25 33 35 41 55 75 77 105 123 165 175 205 231 275 287 385 451 525 615 825 861 1,025 1,155 1,353 1,435 1,681 1,925 2,255 3,075 3,157 4,305 5,043 5,775 6,765 7,175 8,405 9,471 11,275 11,767 15,785 18,491 21,525 25,215 33,825 35,301 42,025 47,355 55,473 58,835 78,925 92,455 126,075 129,437

Collatz Trajectory (119 steps to reach 1)

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

9,707,775 29,123,326 14,561,663 43,684,990 21,842,495 65,527,486 32,763,743 98,291,230 49,145,615 147,436,846 73,718,423 221,155,270 110,577,635 331,732,906 165,866,453 497,599,360 248,799,680 124,399,840 62,199,920 31,099,960 15,549,980 7,774,990 3,887,495 11,662,486 5,831,243 17,493,730 8,746,865 26,240,596 13,120,298 6,560,149 19,680,448 9,840,224 4,920,112 2,460,056 1,230,028 615,014 307,507 922,522 461,261 1,383,784 691,892 345,946 172,973 518,920 259,460 129,730 64,865 194,596 97,298 48,649 145,948 72,974 36,487 109,462 54,731 164,194 82,097 246,292 123,146 61,573

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