

A337372


Primitive terms of A246282: Numbers that are included in that sequence, but none of whose proper divisors are.


9



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
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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 dk, d<k it holds that A003961(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<n)&&A252742(d));
isA337372(n) = ((1==A252742(n))&&(0==A337346(n)));


CROSSREFS

Setwise difference A246282 \ A341610.
Cf. A003961, A246281, A252742, A337346.
Positions of ones in A337345 and in A341609 (characteristic function).
Subsequence of A263837 and thus also of A341614. XXX  Check!
Cf. also A091191, A326134.
Sequence in context: A036326 A078972 A115652 * A317299 A236026 A193305
Adjacent sequences: A337369 A337370 A337371 * A337373 A337374 A337375


KEYWORD

nonn,changed


AUTHOR

Antti Karttunen, Aug 27 2020


STATUS

approved



