λ
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Atlas › Integer Profiles › Node 61,344,129

61,344,129

3 × 72 × 11 × 59 × 643
Deficient Odd Composite

61,344,129 factors as 3 × 7^2 × 11 × 59 × 643. Its 48 positive divisors give a proper-divisor sum of 44,374,911, so this integer is deficient. The Collatz stopping time is 326 steps.

Prime Factor Structure

Factorization String 3 × 7^2 × 11 × 59 × 643
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 105,719,040
Proper Divisor Sum 44,374,911
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #61344121 ← → #61344131

Radix Representation

Decimal 61344129
Binary 11101010000000100110000001 (26 bits)
Octal 0o352004601
Hexadecimal 0x3A80981

Divisor Catalog (48)

1 3 7 11 21 33 49 59 77 147 177 231 413 539 643 649 1,239 1,617 1,929 1,947 2,891 4,501 4,543 7,073 8,673 13,503 13,629 21,219 31,507 31,801 37,937 49,511 94,521 95,403 113,811 148,533 265,559 346,577 417,307 796,677 1,039,731 1,251,921 1,858,913 2,921,149 5,576,739 8,763,447 20,448,043 61,344,129

Collatz Trajectory (326 steps to reach 1)

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

61,344,129 184,032,388 92,016,194 46,008,097 138,024,292 69,012,146 34,506,073 103,518,220 51,759,110 25,879,555 77,638,666 38,819,333 116,458,000 58,229,000 29,114,500 14,557,250 7,278,625 21,835,876 10,917,938 5,458,969 16,376,908 8,188,454 4,094,227 12,282,682 6,141,341 18,424,024 9,212,012 4,606,006 2,303,003 6,909,010 3,454,505 10,363,516 5,181,758 2,590,879 7,772,638 3,886,319 11,658,958 5,829,479 17,488,438 8,744,219 26,232,658 13,116,329 39,348,988 19,674,494 9,837,247 29,511,742 14,755,871 44,267,614 22,133,807 66,401,422 33,200,711 99,602,134 49,801,067 149,403,202 74,701,601 224,104,804 112,052,402 56,026,201 168,078,604 84,039,302

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