λ
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Atlas › Integer Profiles › Node 34,900,420

34,900,420

22 × 5 × 31 × 181 × 311
Abundant Even Composite

34,900,420 factors as 2^2 × 5 × 31 × 181 × 311. Its 48 positive divisors give a proper-divisor sum of 41,417,276, so this integer is abundant. The Collatz stopping time is 152 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 31 × 181 × 311
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 76,317,696
Proper Divisor Sum 41,417,276
Digit Sum / Digital Root 22 (Root: 4)
Adjacent Primes #34900403 ← → #34900423

Radix Representation

Decimal 34900420
Binary 10000101001000100111000100 (26 bits)
Octal 0o205104704
Hexadecimal 0x21489C4

Divisor Catalog (48)

1 2 4 5 10 20 31 62 124 155 181 310 311 362 620 622 724 905 1,244 1,555 1,810 3,110 3,620 5,611 6,220 9,641 11,222 19,282 22,444 28,055 38,564 48,205 56,110 56,291 96,410 112,220 112,582 192,820 225,164 281,455 562,910 1,125,820 1,745,021 3,490,042 6,980,084 8,725,105 17,450,210 34,900,420

Collatz Trajectory (152 steps to reach 1)

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

34,900,420 17,450,210 8,725,105 26,175,316 13,087,658 6,543,829 19,631,488 9,815,744 4,907,872 2,453,936 1,226,968 613,484 306,742 153,371 460,114 230,057 690,172 345,086 172,543 517,630 258,815 776,446 388,223 1,164,670 582,335 1,747,006 873,503 2,620,510 1,310,255 3,930,766 1,965,383 5,896,150 2,948,075 8,844,226 4,422,113 13,266,340 6,633,170 3,316,585 9,949,756 4,974,878 2,487,439 7,462,318 3,731,159 11,193,478 5,596,739 16,790,218 8,395,109 25,185,328 12,592,664 6,296,332 3,148,166 1,574,083 4,722,250 2,361,125 7,083,376 3,541,688 1,770,844 885,422 442,711 1,328,134

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