λ
Ratio Atlas
Atlas › Integer Profiles › Node 78,200,031
78,200,031
3 × 72 × 13 × 151 × 271
Deficient Odd Composite

Prime Factor Structure

Factorization String 3 × 7^2 × 13 × 151 × 271
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 131,970,048
Proper Divisor Sum 53,770,017
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #78199999 ← → #78200033

Radix Representation

Decimal 78200031
Binary 100101010010011110011011111 (27 bits)
Octal 0o452236337
Hexadecimal 0x4A93CDF

Divisor Catalog (48)

1 3 7 13 21 39 49 91 147 151 271 273 453 637 813 1,057 1,897 1,911 1,963 3,171 3,523 5,691 5,889 7,399 10,569 13,279 13,741 22,197 24,661 39,837 40,921 41,223 73,983 96,187 122,763 172,627 286,447 288,561 517,881 531,973 859,341 1,595,919 2,005,129 3,723,811 6,015,387 11,171,433 26,066,677 78,200,031

Collatz Trajectory (179 steps to reach 1)

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

78,200,031 234,600,094 117,300,047 351,900,142 175,950,071 527,850,214 263,925,107 791,775,322 395,887,661 1,187,662,984 593,831,492 296,915,746 148,457,873 445,373,620 222,686,810 111,343,405 334,030,216 167,015,108 83,507,554 41,753,777 125,261,332 62,630,666 31,315,333 93,946,000 46,973,000 23,486,500 11,743,250 5,871,625 17,614,876 8,807,438 4,403,719 13,211,158 6,605,579 19,816,738 9,908,369 29,725,108 14,862,554 7,431,277 22,293,832 11,146,916 5,573,458 2,786,729 8,360,188 4,180,094 2,090,047 6,270,142 3,135,071 9,405,214 4,702,607 14,107,822 7,053,911 21,161,734 10,580,867 31,742,602 15,871,301 47,613,904 23,806,952 11,903,476 5,951,738 2,975,869

Active Feeder Network

Other feeder batches with open delivery windows. Each feeder keeps its own target batch.

Feeder #6,573,969 Feeder #6,845,105 Feeder #8,750,980 Feeder #906,051 Feeder #1,285,993 Feeder #7,584,379 Feeder #4,761,186 Feeder #626,174
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