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A348034
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Numbers k that have at least one unitary divisor d such that sigma(d)*d is equal to k.
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2
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1, 6, 12, 28, 30, 56, 117, 120, 132, 182, 306, 380, 496, 552, 672, 775, 870, 992, 1080, 1406, 1680, 1722, 1892, 2016, 2184, 2256, 2793, 2862, 3276, 3540, 3782, 3960, 4556, 4560, 4650, 5112, 5402, 5460, 6320, 6552, 6972, 7392, 8010, 8128, 9180, 9300, 9506, 9801, 10302, 10712, 11556, 11904, 11990, 12882, 16093, 16256
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OFFSET
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1,2
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LINKS
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EXAMPLE
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120 = 2^3 * 3 * 5 has a unitary divisor 8 for which sigma(8) = 15 = 120/8, thus 120 is included in the sequence.
672 = 2^5 * 3 * 7 has a unitary divisor 21 for which sigma(21) = 32 = 120/21, thus 672 is included in the sequence.
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MATHEMATICA
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q[n_] := DivisorSum[n, 1 &, CoprimeQ[#, n/#] && #*DivisorSigma[1, #] == n &] > 0; Select[Range[16256], q] (* Amiram Eldar, Sep 27 2021 *)
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PROG
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(PARI) isA348034(n) = { fordiv(n, d, if(1==gcd(d, n/d)&&n==d*sigma(d), return(1))); (0); };
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CROSSREFS
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Positions of nonzero terms in A348033.
Cf. also A348035 (multiply-perfect numbers in this sequence).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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