λ
Harmonic Matrix
Atlas › Integer Profiles › Node 4,074,759

4,074,759

33 × 132 × 19 × 47
Deficient Odd Composite

4,074,759 has digital root 9. The neighboring primes are 4074757 and 4074767; its proper-divisor sum differs from the starting integer by -1,122,318.

Prime Factor Structure

Factorization String 3^3 × 13^2 × 19 × 47
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 7,027,200
Proper Divisor Sum 2,952,441
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #4074757 ← → #4074767

Radix Representation

Decimal 4074759
Binary 1111100010110100000111 (22 bits)
Octal 0o17426407
Hexadecimal 0x3E2D07

Divisor Catalog (48)

1 3 9 13 19 27 39 47 57 117 141 169 171 247 351 423 507 513 611 741 893 1,269 1,521 1,833 2,223 2,679 3,211 4,563 5,499 6,669 7,943 8,037 9,633 11,609 16,497 23,829 24,111 28,899 34,827 71,487 86,697 104,481 150,917 214,461 313,443 452,751 1,358,253 4,074,759

Collatz Trajectory (198 steps to reach 1)

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

4,074,759 12,224,278 6,112,139 18,336,418 9,168,209 27,504,628 13,752,314 6,876,157 20,628,472 10,314,236 5,157,118 2,578,559 7,735,678 3,867,839 11,603,518 5,801,759 17,405,278 8,702,639 26,107,918 13,053,959 39,161,878 19,580,939 58,742,818 29,371,409 88,114,228 44,057,114 22,028,557 66,085,672 33,042,836 16,521,418 8,260,709 24,782,128 12,391,064 6,195,532 3,097,766 1,548,883 4,646,650 2,323,325 6,969,976 3,484,988 1,742,494 871,247 2,613,742 1,306,871 3,920,614 1,960,307 5,880,922 2,940,461 8,821,384 4,410,692 2,205,346 1,102,673 3,308,020 1,654,010 827,005 2,481,016 1,240,508 620,254 310,127 930,382

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