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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A007504, A014285, A306834, A309036.

Sequence in context: A263881 A208892 A085397 * A073439 A188084 A242750

Adjacent sequences: A307411 A307412 A307413 * A307415 A307416 A307417

Keyword

nonn

Author

Robert Israel, Apr 07 2019

Status

approved