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Atlas › Integer Profiles › Node 4,077,948

4,077,948

22 × 3 × 7 × 43 × 1129
Abundant Even Composite

4,077,948 factors as 2^2 × 3 × 7 × 43 × 1129. Its 48 positive divisors give a proper-divisor sum of 7,059,332, so this integer is abundant. The Collatz stopping time is 136 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 43 × 1129
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 11,137,280
Proper Divisor Sum 7,059,332
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #4077947 ← → #4077949

Radix Representation

Decimal 4077948
Binary 1111100011100101111100 (22 bits)
Octal 0o17434574
Hexadecimal 0x3E397C

Divisor Catalog (48)

1 2 3 4 6 7 12 14 21 28 42 43 84 86 129 172 258 301 516 602 903 1,129 1,204 1,806 2,258 3,387 3,612 4,516 6,774 7,903 13,548 15,806 23,709 31,612 47,418 48,547 94,836 97,094 145,641 194,188 291,282 339,829 582,564 679,658 1,019,487 1,359,316 2,038,974 4,077,948

Collatz Trajectory (136 steps to reach 1)

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

4,077,948 2,038,974 1,019,487 3,058,462 1,529,231 4,587,694 2,293,847 6,881,542 3,440,771 10,322,314 5,161,157 15,483,472 7,741,736 3,870,868 1,935,434 967,717 2,903,152 1,451,576 725,788 362,894 181,447 544,342 272,171 816,514 408,257 1,224,772 612,386 306,193 918,580 459,290 229,645 688,936 344,468 172,234 86,117 258,352 129,176 64,588 32,294 16,147 48,442 24,221 72,664 36,332 18,166 9,083 27,250 13,625 40,876 20,438 10,219 30,658 15,329 45,988 22,994 11,497 34,492 17,246 8,623 25,870

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