λ
Harmonic Matrix

6,148,072

23 × 7 × 101 × 1087
Abundant Even Composite

6,148,072 has digital root 1. The neighboring primes are 6148069 and 6148091; its proper-divisor sum differs from the starting integer by 1,020,976.

Prime Factor Structure

Factorization String 2^3 × 7 × 101 × 1087
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 13,317,120
Proper Divisor Sum 7,169,048
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #6148069 ← → #6148091

Radix Representation

Decimal 6148072
Binary 10111011100111111101000 (23 bits)
Octal 0o27347750
Hexadecimal 0x5DCFE8

Divisor Catalog (32)

1 2 4 7 8 14 28 56 101 202 404 707 808 1,087 1,414 2,174 2,828 4,348 5,656 7,609 8,696 15,218 30,436 60,872 109,787 219,574 439,148 768,509 878,296 1,537,018 3,074,036 6,148,072

Collatz Trajectory (165 steps to reach 1)

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

6,148,072 3,074,036 1,537,018 768,509 2,305,528 1,152,764 576,382 288,191 864,574 432,287 1,296,862 648,431 1,945,294 972,647 2,917,942 1,458,971 4,376,914 2,188,457 6,565,372 3,282,686 1,641,343 4,924,030 2,462,015 7,386,046 3,693,023 11,079,070 5,539,535 16,618,606 8,309,303 24,927,910 12,463,955 37,391,866 18,695,933 56,087,800 28,043,900 14,021,950 7,010,975 21,032,926 10,516,463 31,549,390 15,774,695 47,324,086 23,662,043 70,986,130 35,493,065 106,479,196 53,239,598 26,619,799 79,859,398 39,929,699 119,789,098 59,894,549 179,683,648 89,841,824 44,920,912 22,460,456 11,230,228 5,615,114 2,807,557 8,422,672

More profiles

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