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A258912
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Numbers k such that A000203(x) = k has more than one solution and they all share the same largest prime factor.
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1
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1178, 1364, 1408, 1656, 1767, 1836, 1922, 1984, 2108, 2196, 2328, 2368, 3162, 3336, 3410, 3996, 4096, 4123, 4144, 4278, 4898, 5064, 5076, 5084, 5248, 5456, 5488, 5673, 6014, 6208, 6504, 6784, 6816, 7416, 7998, 8618, 8896, 9088, 9184, 9517, 10048, 10292, 10864
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OFFSET
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1,1
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COMMENTS
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By definition this is a subsequence of A159886.
Pollack shows that the density of such integers relative to A002191 is 1.
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LINKS
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EXAMPLE
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The pre-image of 1178 is [592, 925], and both have greatest prime factor 37, so 1178 is in the sequence.
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PROG
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(PARI) isok(n) = {my(v = select(x->sigma(x)==n, vector(n, i, i))); if (#v < 2, return (0)); vgpf = vector(#v, k, fvk = factor(v[k]); fvk[#fvk~, 1]); vecmin(vgpf) == vecmax(vgpf); }
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CROSSREFS
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Cf. A000203 (sum of divisors), A002191 (possible values of sum of divisors), A159886 (sigma(x)=n has more than one solution).
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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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