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Atlas › Integer Profiles › Node 34,676,980

34,676,980

22 × 5 × 13 × 41 × 3253
Abundant Even Composite

34,676,980 factors as 2^2 × 5 × 13 × 41 × 3253. Its 48 positive divisors give a proper-divisor sum of 45,683,804, so this integer is abundant. The Collatz stopping time is 152 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 13 × 41 × 3253
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 80,360,784
Proper Divisor Sum 45,683,804
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #34676977 ← → #34676987

Radix Representation

Decimal 34676980
Binary 10000100010010000011110100 (26 bits)
Octal 0o204220364
Hexadecimal 0x21120F4

Divisor Catalog (48)

1 2 4 5 10 13 20 26 41 52 65 82 130 164 205 260 410 533 820 1,066 2,132 2,665 3,253 5,330 6,506 10,660 13,012 16,265 32,530 42,289 65,060 84,578 133,373 169,156 211,445 266,746 422,890 533,492 666,865 845,780 1,333,730 1,733,849 2,667,460 3,467,698 6,935,396 8,669,245 17,338,490 34,676,980

Collatz Trajectory (152 steps to reach 1)

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

34,676,980 17,338,490 8,669,245 26,007,736 13,003,868 6,501,934 3,250,967 9,752,902 4,876,451 14,629,354 7,314,677 21,944,032 10,972,016 5,486,008 2,743,004 1,371,502 685,751 2,057,254 1,028,627 3,085,882 1,542,941 4,628,824 2,314,412 1,157,206 578,603 1,735,810 867,905 2,603,716 1,301,858 650,929 1,952,788 976,394 488,197 1,464,592 732,296 366,148 183,074 91,537 274,612 137,306 68,653 205,960 102,980 51,490 25,745 77,236 38,618 19,309 57,928 28,964 14,482 7,241 21,724 10,862 5,431 16,294 8,147 24,442 12,221 36,664

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