A119379 Untouchable semiprimes: semiprimes which are not the sum of the aliquot parts of any number.

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

Offset: 1

Author

Tanya Khovanova, Jul 24 2006

Keywords

• nonn

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).

Crossrefs

Intersection of A001358 and A005114.

Programs

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 *)

Extensions

More terms from Franklin T. Adams-Watters and Don Reble, Jul 28 2006