λ
Harmonic Matrix

1,360,120

23 × 5 × 37 × 919
Abundant Even Composite

1,360,120 has digital root 4. The neighboring primes are 1360103 and 1360141; its proper-divisor sum differs from the starting integer by 426,160.

Prime Factor Structure

Factorization String 2^3 × 5 × 37 × 919
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 3,146,400
Proper Divisor Sum 1,786,280
Digit Sum / Digital Root 13 (Root: 4)
Adjacent Primes #1360103 ← → #1360141

Radix Representation

Decimal 1360120
Binary 101001100000011111000 (21 bits)
Octal 0o5140370
Hexadecimal 0x14C0F8

Divisor Catalog (32)

1 2 4 5 8 10 20 37 40 74 148 185 296 370 740 919 1,480 1,838 3,676 4,595 7,352 9,190 18,380 34,003 36,760 68,006 136,012 170,015 272,024 340,030 680,060 1,360,120

Collatz Trajectory (186 steps to reach 1)

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

1,360,120 680,060 340,030 170,015 510,046 255,023 765,070 382,535 1,147,606 573,803 1,721,410 860,705 2,582,116 1,291,058 645,529 1,936,588 968,294 484,147 1,452,442 726,221 2,178,664 1,089,332 544,666 272,333 817,000 408,500 204,250 102,125 306,376 153,188 76,594 38,297 114,892 57,446 28,723 86,170 43,085 129,256 64,628 32,314 16,157 48,472 24,236 12,118 6,059 18,178 9,089 27,268 13,634 6,817 20,452 10,226 5,113 15,340 7,670 3,835 11,506 5,753 17,260 8,630

More profiles

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