A309036 -id:A309036 - cp's OEIS frontend

A309055 Record values of A309036.

2, 17, 20, 43, 107, 142, 176, 1291, 1748, 3309, 5114, 9412, 13032, 53799, 62195, 258834, 515752, 590919, 1880056, 4387977, 4982469, 8725487, 10021836, 22701799, 34769113, 75672055, 3847032954, 6476460401, 8607624876, 13054048917, 40404144055, 55300901872

Offset: 1

Robert Israel, Jul 09 2019

nonn

			a(3) = 20 is a term because A309036(25) = 20 and A309036(k) < 20 for k < 25.

Giovanni Resta, Table of n, a(n) for n = 1..37

Cf. A309036, A309056.

S1:= 0: S2:= 0: Recv:= NULL: count:= 0:
maxv:= 0:
for n from 1 to 200000 do
  p:= ithprime(n);
  S1:= S1 + p;
  S2:= S2 + n*p;
  v:= igcd(S1, S2);
  if v > maxv then
    maxv:= v;
    count:= count+1;
    Recv:= Recv,v;
  fi
od:
Recv;

lista(nn) = {my(k=r=s=t=0); forprime(p=2, nn, if(gcd(s+=p, t+=(k++)*p)>r, r=gcd(s,t); print1(r, ", "))); } \\ Jinyuan Wang, Apr 16 2020

a(n) = A309036(A309056(n)).

a(16)-a(27) from Rémy Sigrist, Jul 09 2019
a(28) from Jinyuan Wang, Apr 16 2020
Terms a(29) and beyond from Giovanni Resta, Apr 19 2020

A309056 Where records of A309036 occur.

Original entry on oeis.org

1, 4, 25, 26, 43, 77, 201, 336, 881, 2144, 22305, 24113, 44349, 48748, 153884, 400161, 793873, 1195455, 5066329, 6227954, 11394871, 16233979, 18368369, 63843903, 80998288, 117335658, 246252769, 6420049930, 23198011949, 30432298548, 62709861290, 117888644809

Offset: 1

Robert Israel, Jul 09 2019

nonn

Numbers m such that A309036(m) > A309036(k) for all k < m.

			a(3) = 25 is a term because A309036(25) = 20 and A309036(k) < 20 for k < 25.

Giovanni Resta, Table of n, a(n) for n = 1..37

Cf. A309036, A309055.

S1:= 0: S2:= 0: Recn:= NULL: count:= 0:
maxv:= 0:
for n from 1 to 200000 do
  p:= ithprime(n);
  S1:= S1 + p;
  S2:= S2 + n*p;
  v:= igcd(S1, S2);
  if v > maxv then
    maxv:= v;
    count:= count+1;
    Recn:= Recn, n;
  fi
od:
Recn;

lista(nn) = {my(k=r=s=t=0); forprime(p=2, nn, if(gcd(s+=p, t+=(k++)*p)>r, r=gcd(s,t); print1(k, ", "))); } \\ Jinyuan Wang, Apr 16 2020

A309055(n) = A309036(a(n)).

a(16)-a(27) from Rémy Sigrist, Jul 09 2019
a(28) from Jinyuan Wang, Apr 16 2020
Terms a(29) and beyond from Giovanni Resta, Apr 19 2020

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

Original entry on oeis.org

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

Robert Israel, Apr 07 2019

nonn

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

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

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

Cf. A007504, A014285, A306834, A309036.

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]);

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

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

cp's OEIS Frontend

A309055 Record values of A309036.

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A309056 Where records of A309036 occur.

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Author

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Examples

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Crossrefs

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Maple

PARI

Formula

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI