414,141

3 × 7 × 13 × 37 × 41

414,141 factors as 3 × 7 × 13 × 37 × 41. Its 32 positive divisors give a proper-divisor sum of 300,867, so this integer is deficient. The Collatz stopping time is 81 steps.

Prime Factor Structure

Factorization String 3 × 7 × 13 × 37 × 41

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 715,008

Proper Divisor Sum 300,867

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #414131 ← → #414157

Radix Representation

Decimal	414141
Binary	1100101000110111101 (19 bits)
Octal	0o1450675
Hexadecimal	0x651BD

Divisor Catalog (32)

1 3 7 13 21 37 39 41 91 111 123 259 273 287 481 533 777 861 1,443 1,517 1,599 3,367 3,731 4,551 10,101 10,619 11,193 19,721 31,857 59,163 138,047 414,141

Collatz Trajectory (81 steps to reach 1)

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

414,141 1,242,424 621,212 310,606 155,303 465,910 232,955 698,866 349,433 1,048,300 524,150 262,075 786,226 393,113 1,179,340 589,670 294,835 884,506 442,253 1,326,760 663,380 331,690 165,845 497,536 248,768 124,384 62,192 31,096 15,548 7,774 3,887 11,662 5,831 17,494 8,747 26,242 13,121 39,364 19,682 9,841 29,524 14,762 7,381 22,144 11,072 5,536 2,768 1,384 692 346 173 520 260 130 65 196 98 49 148 74

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