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Unitary perfect number
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==Known examples== The number [[60 (number)|60]] is a unitary perfect number because 1, 3, 4, 5, 12, 15, and 20 are its proper unitary divisors, and 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60. The first five, and only known, unitary perfect numbers are: * <math>6 = 2 \times 3</math> * <math>60 = 2^2 \times 3 \times 5</math> * <math>90 = 2 \times 3^2 \times 5</math> * <math>87360 = 2^6 \times 3 \times 5 \times 7 \times 13</math>, and *<math>146361946186458562560000 = 2^{18} \times 3 \times 5^4 \times 7 \times 11 \times 13 \times 19 \times 37 \times 79 \times 109 \times 157 \times 313</math> {{OEIS|id=A002827}}. The respective sums of their proper unitary divisors are as follows: * [[6 (number)|6]] = 1 + 2 + 3 * 60 = 1 + 3 + 4 + 5 + 12 + 15 + 20 * [[90 (number)|90]] = 1 + 2 + 5 + 9 + 10 + 18 + 45 * 87360 = 1 + 3 + 5 + 7 + 13 + 15 + 21 + 35 + 39 + 64 + 65 + 91 + 105 + 192 + 195 + 273 + 320 + 448 + 455 + 832 + 960 + 1344 + 1365 + 2240 + 2496 + 4160 + 5824 + 6720 + 12480 + 17472 + 29120 * 146361946186458562560000 = 1 + 3 + 7 + 11 + ... + 13305631471496232960000 + 20908849455208366080000 + 48787315395486187520000 (4095 divisors in the sum)
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