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%I #24 Mar 06 2021 01:33:41
%S 4,6,9,10,14,15,21,35,39,49,57,69,91,125,242,275,286,325,338,363,418,
%T 425,442,475,494,506,561,575,598,646,682,715,722,725,754,775,782,806,
%U 845,847,867,874,925,957,962,1023,1025,1045,1054,1058,1066,1075,1105,1118,1175,1178,1221,1222,1235,1265,1309,1325,1334,1353
%N Primitive terms of A246282: Numbers that are included in that sequence, but none of whose proper divisors are.
%C Numbers k whose only divisor in A246282 is k itself, i.e., A003961(k) > 2k, but for none of the proper divisors d|k, d<k it holds that A003961(d) > 2d.
%C Question: Do the odd terms in A326134 all occur here? Answer is yes, if the following conjecture holds: This is a subsequence of A263837, nonabundant numbers. In other words, we claim that any abundant number k (A005101) has A337345(k) > 1 and thus is a term of A341610.
%H Antti Karttunen, <a href="/A337372/b337372.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F {k: 1==A337345(k)}.
%t Block[{a = {}, b = {}}, Do[If[2 i < Times @@ Map[#1^#2 & @@ # &, FactorInteger[i] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[i == 1], AppendTo[a, i]; If[IntersectingQ[Most@ Divisors[i], a], AppendTo[b, i]]], {i, 1400}]; Complement[a, b]] (* _Michael De Vlieger_, Feb 22 2021 *)
%o (PARI)
%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A252742(n) = (A003961(n) > (2*n));
%o A337346(n) = sumdiv(n,d,(d<n)&&A252742(d));
%o isA337372(n) = ((1==A252742(n))&&(0==A337346(n)));
%Y Setwise difference A246282 \ A341610.
%Y Cf. A003961, A246281, A252742, A337346.
%Y Positions of ones in A337345 and in A341609 (characteristic function).
%Y Subsequence of A263837 and thus also of A341614. XXX - Check!
%Y Cf. also A091191, A326134.
%K nonn
%O 1,1
%A _Antti Karttunen_, Aug 27 2020
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