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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
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.)