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Atlas › Integer Profiles › Node 27,972,777

27,972,777

3 × 72 × 372 × 139
Deficient Odd Composite

Prime Factor Structure

Factorization String 3 × 7^2 × 37^2 × 139
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 44,911,440
Proper Divisor Sum 16,938,663
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #27972773 ← → #27972781

Radix Representation

Decimal 27972777
Binary 1101010101101010010101001 (25 bits)
Octal 0o152552251
Hexadecimal 0x1AAD4A9

Divisor Catalog (36)

1 3 7 21 37 49 111 139 147 259 417 777 973 1,369 1,813 2,919 4,107 5,143 5,439 6,811 9,583 15,429 20,433 28,749 36,001 67,081 108,003 190,291 201,243 252,007 570,873 756,021 1,332,037 3,996,111 9,324,259 27,972,777

Collatz Trajectory (291 steps to reach 1)

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

27,972,777 83,918,332 41,959,166 20,979,583 62,938,750 31,469,375 94,408,126 47,204,063 141,612,190 70,806,095 212,418,286 106,209,143 318,627,430 159,313,715 477,941,146 238,970,573 716,911,720 358,455,860 179,227,930 89,613,965 268,841,896 134,420,948 67,210,474 33,605,237 100,815,712 50,407,856 25,203,928 12,601,964 6,300,982 3,150,491 9,451,474 4,725,737 14,177,212 7,088,606 3,544,303 10,632,910 5,316,455 15,949,366 7,974,683 23,924,050 11,962,025 35,886,076 17,943,038 8,971,519 26,914,558 13,457,279 40,371,838 20,185,919 60,557,758 30,278,879 90,836,638 45,418,319 136,254,958 68,127,479 204,382,438 102,191,219 306,573,658 153,286,829 459,860,488 229,930,244

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