417,879

3⁴ × 7 × 11 × 67

417,879 factors as 3^4 × 7 × 11 × 67. Its 40 positive divisors give a proper-divisor sum of 372,009, so this integer is deficient. The Collatz stopping time is 174 steps.

Prime Factor Structure

Factorization String 3^4 × 7 × 11 × 67

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 789,888

Proper Divisor Sum 372,009

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #417869 ← → #417881

Radix Representation

Decimal	417879
Binary	1100110000001010111 (19 bits)
Octal	0o1460127
Hexadecimal	0x66057

Divisor Catalog (40)

1 3 7 9 11 21 27 33 63 67 77 81 99 189 201 231 297 469 567 603 693 737 891 1,407 1,809 2,079 2,211 4,221 5,159 5,427 6,237 6,633 12,663 15,477 19,899 37,989 46,431 59,697 139,293 417,879

Collatz Trajectory (174 steps to reach 1)

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

417,879 1,253,638 626,819 1,880,458 940,229 2,820,688 1,410,344 705,172 352,586 176,293 528,880 264,440 132,220 66,110 33,055 99,166 49,583 148,750 74,375 223,126 111,563 334,690 167,345 502,036 251,018 125,509 376,528 188,264 94,132 47,066 23,533 70,600 35,300 17,650 8,825 26,476 13,238 6,619 19,858 9,929 29,788 14,894 7,447 22,342 11,171 33,514 16,757 50,272 25,136 12,568 6,284 3,142 1,571 4,714 2,357 7,072 3,536 1,768 884 442

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