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 A337372 Primitive terms of A246282: Numbers that are included in that sequence, but none of whose proper divisors are. 11
 4, 6, 9, 10, 14, 15, 21, 35, 39, 49, 57, 69, 91, 125, 242, 275, 286, 325, 338, 363, 418, 425, 442, 475, 494, 506, 561, 575, 598, 646, 682, 715, 722, 725, 754, 775, 782, 806, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 2d. 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. LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 Index entries for sequences computed from indices in prime factorization FORMULA {k: 1==A337345(k)}. MATHEMATICA 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 *) PROG (PARI) A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A252742(n) = (A003961(n) > (2*n)); A337346(n) = sumdiv(n, d, (d

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Last modified September 13 04:07 EDT 2024. Contains 375859 sequences. (Running on oeis4.)