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Atlas › Integer Profiles › Node 34,254,688

34,254,688

25 × 13 × 67 × 1229
Abundant Even Composite

34,254,688 factors as 2^5 × 13 × 67 × 1229. Its 48 positive divisors give a proper-divisor sum of 39,515,792, so this integer is abundant. The Collatz stopping time is 100 steps.

Prime Factor Structure

Factorization String 2^5 × 13 × 67 × 1229
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 73,770,480
Proper Divisor Sum 39,515,792
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #34254683 ← → #34254697

Radix Representation

Decimal 34254688
Binary 10000010101010111101100000 (26 bits)
Octal 0o202527540
Hexadecimal 0x20AAF60

Divisor Catalog (48)

1 2 4 8 13 16 26 32 52 67 104 134 208 268 416 536 871 1,072 1,229 1,742 2,144 2,458 3,484 4,916 6,968 9,832 13,936 15,977 19,664 27,872 31,954 39,328 63,908 82,343 127,816 164,686 255,632 329,372 511,264 658,744 1,070,459 1,317,488 2,140,918 2,634,976 4,281,836 8,563,672 17,127,344 34,254,688

Collatz Trajectory (100 steps to reach 1)

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

34,254,688 17,127,344 8,563,672 4,281,836 2,140,918 1,070,459 3,211,378 1,605,689 4,817,068 2,408,534 1,204,267 3,612,802 1,806,401 5,419,204 2,709,602 1,354,801 4,064,404 2,032,202 1,016,101 3,048,304 1,524,152 762,076 381,038 190,519 571,558 285,779 857,338 428,669 1,286,008 643,004 321,502 160,751 482,254 241,127 723,382 361,691 1,085,074 542,537 1,627,612 813,806 406,903 1,220,710 610,355 1,831,066 915,533 2,746,600 1,373,300 686,650 343,325 1,029,976 514,988 257,494 128,747 386,242 193,121 579,364 289,682 144,841 434,524 217,262

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