A307414 Numbers k such that A014285(k) and A007504(k) are coprime.

2, 3, 6, 7, 10, 11, 12, 14, 15, 18, 19, 22, 23, 24, 27, 30, 31, 32, 34, 35, 38, 39, 40, 44, 46, 47, 48, 51, 52, 55, 56, 58, 59, 60, 63, 64, 66, 67, 70, 71, 72, 74, 75, 76, 78, 79, 82, 83, 86, 87, 88, 91, 92, 94, 95, 96, 98, 99, 100, 102, 104, 106, 108, 110, 112, 114, 115, 116, 118, 119, 120, 122

Offset: 1

Author

Robert Israel, Apr 07 2019

Keywords

• nonn

Comments

Numbers k such that A306834(k) = A014285(k).

No terms == 1 (mod 4).

Numbers k such that A309036(k)=1. - Robert Israel, Jul 09 2019

Examples

			a(3) = 6 is a term because A007504(6) = 41 and A014285(6) = 184 are coprime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A014285, A306834, A309036.

Programs

Maple

N:= 1000: # for terms <= N
Primes:= map(ithprime, [$1..N]):
S1:= ListTools:-PartialSums(Primes):
S2:= ListTools:-PartialSums(zip(`*`,Primes, [$1..N])):
select(t -> igcd(S1[t],S2[t])=1, [$1..N]);

Mathematica

okQ[n_] := With[{pp = Prime[Range[n]]}, CoprimeQ[Total[pp], Total[pp.Range[n]]]];
Select[Range[200], okQ] (* Jean-François Alcover, Dec 05 2023 *)

PARI

isok(k) = my(vp=primes(k)); gcd(sum(i=1, k, vp[i]), sum(i=1, k, i*vp[i])) == 1; \\ Michel Marcus, Apr 07 2019