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 A119379 Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Amiram Eldar, Feb 13 2021: (Start) 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). LINKS Amiram Eldar, Table of n, a(n) for n = 1..9035 (terms below 10^6, calculated using data from Giovanni Resta; terms 1..1000 from Donovan Johnson) Jack David Alanen, Empirical study of aliquot series, Ph.D Thesis, Yale University, 1972. Giovanni Resta, Untouchable numbers (includes a list of the 150232 untouchable numbers below 10^6). MATHEMATICA 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 *) CROSSREFS Intersection of A001358 and A005114. Sequence in context: A248406 A135666 A365202 * A118699 A238579 A238028 Adjacent sequences: A119376 A119377 A119378 * A119380 A119381 A119382 KEYWORD nonn AUTHOR Tanya Khovanova, Jul 24 2006 EXTENSIONS More terms from Franklin T. Adams-Watters and Don Reble, Jul 28 2006 STATUS approved

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Last modified April 16 21:50 EDT 2024. Contains 371755 sequences. (Running on oeis4.)