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A119379
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Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number.
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2
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146, 206, 262, 326, 562, 626, 718, 766, 802, 818, 898, 926, 934, 982, 1046, 1186, 1318, 1346, 1418, 1438, 1522, 1538, 1642, 1718, 1766, 1774, 1822, 1838, 1894, 2062, 2078, 2098, 2174, 2218, 2258, 2302, 2306, 2446, 2498, 2518, 2602, 2606, 2614, 2642, 2762
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OFFSET
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1,1
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COMMENTS
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Assuming that 5 is the only odd untouchable number, all the terms are of the form 2*p, where p is a prime.
Alanen (1972) calculated the first 70 terms of this sequence (terms below 5000). (End).
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LINKS
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Giovanni Resta, Untouchable numbers (includes a list of the 150232 untouchable numbers below 10^6).
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MATHEMATICA
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seq[max_] := Module[{v = Table[0, {max}]}, Do[k = DivisorSigma[1, n] - n; If[2 <= k <= max, v[[k]]++], {n, 1, max^2}]; Select[Rest[Position[v, _?(# == 0 &)] // Flatten], PrimeOmega[#] == 2 &]]; seq[1000] (* Amiram Eldar, Feb 13 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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