λ
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Atlas › Integer Profiles › Node 51,577,630

51,577,630

2 × 5 × 13 × 37 × 10723
Deficient Even Composite

51,577,630 factors as 2 × 5 × 13 × 37 × 10723. Its 32 positive divisors give a proper-divisor sum of 51,115,394, so this integer is deficient. The Collatz stopping time is 212 steps.

Prime Factor Structure

Factorization String 2 × 5 × 13 × 37 × 10723
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 102,693,024
Proper Divisor Sum 51,115,394
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #51577627 ← → #51577633

Radix Representation

Decimal 51577630
Binary 11000100110000001100011110 (26 bits)
Octal 0o304601436
Hexadecimal 0x313031E

Divisor Catalog (32)

1 2 5 10 13 26 37 65 74 130 185 370 481 962 2,405 4,810 10,723 21,446 53,615 107,230 139,399 278,798 396,751 696,995 793,502 1,393,990 1,983,755 3,967,510 5,157,763 10,315,526 25,788,815 51,577,630

Collatz Trajectory (212 steps to reach 1)

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

51,577,630 25,788,815 77,366,446 38,683,223 116,049,670 58,024,835 174,074,506 87,037,253 261,111,760 130,555,880 65,277,940 32,638,970 16,319,485 48,958,456 24,479,228 12,239,614 6,119,807 18,359,422 9,179,711 27,539,134 13,769,567 41,308,702 20,654,351 61,963,054 30,981,527 92,944,582 46,472,291 139,416,874 69,708,437 209,125,312 104,562,656 52,281,328 26,140,664 13,070,332 6,535,166 3,267,583 9,802,750 4,901,375 14,704,126 7,352,063 22,056,190 11,028,095 33,084,286 16,542,143 49,626,430 24,813,215 74,439,646 37,219,823 111,659,470 55,829,735 167,489,206 83,744,603 251,233,810 125,616,905 376,850,716 188,425,358 94,212,679 282,638,038 141,319,019 423,957,058

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