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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 (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<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

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Last modified March 8 07:58 EST 2021. Contains 341941 sequences. (Running on oeis4.)