A073324 -id:A073324 - cp's OEIS frontend

A072548 a(n) = sigma(n) mod PrimePi(n).

0, 0, 1, 0, 0, 0, 3, 1, 2, 2, 3, 2, 0, 0, 1, 4, 4, 4, 2, 0, 4, 6, 6, 4, 6, 4, 2, 0, 2, 10, 8, 4, 10, 4, 3, 2, 0, 8, 6, 3, 5, 2, 0, 8, 2, 3, 4, 12, 3, 12, 8, 6, 8, 8, 8, 0, 10, 9, 15, 8, 6, 14, 1, 12, 0, 11, 12, 1, 11, 12, 15, 11, 9, 19, 14, 12, 0, 14, 10, 11, 16, 15, 17, 16, 17, 5, 19, 18, 18

Offset: 2

Labos Elemer, Aug 05 2002

nonn

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Cf. A000203, A000720, A073321, A073322, A073323, A073324.

[SumOfDivisors(n) mod (#PrimesUpTo(n)): n in [2..100]]; // Vincenzo Librandi, Dec 10 2018

with(numtheory): seq(modp(sigma(n),pi(n)),n=2..100); # Muniru A Asiru, Dec 10 2018

Table[Mod[DivisorSigma[1, w], PrimePi[w]], {w, 1, 128}]

a(n) = sigma(n) % primepi(n); \\ Michel Marcus, Dec 10 2018

a(n) = A000203(n) mod A000720(n).

A073325 a(n) = least k > 0 such that prime(k) == n (mod k).

Original entry on oeis.org

1, 2, 3, 4, 75, 9, 79, 18, 17, 10, 19, 20, 91, 22, 23, 41, 83, 24, 16049, 43, 2711, 94, 25, 26, 95, 198, 449, 452, 99, 50, 451, 48, 453, 1072, 447, 54, 16043, 55, 2719, 56, 459, 57, 101, 472, 100371, 62, 105, 102, 103, 104, 467, 110, 107, 65, 109, 63, 115, 118, 117

Offset: 1

Labos Elemer, Jul 30 2002

nonn

First appearance of n-1 in A004648. Are all positive integers present in A004648 and hence in this sequence? - Zak Seidov, Sep 02 2012

			a(4) = 75 as prime(75) = 379 == 4 (mod 75).
a(44) = 100371 since prime(100371) = 1304867 == 44 (mod 100371) and prime(k) <> 44 (mod k) for k < 100371.

Zak Seidov, Table of n, a(n) for n = 1..301

Cf. A000040, A002808, A004648, A073324, A073326.

nn = 60; f[x_] := Mod[Prime[x], x]; t = Table[0, {nn}]; k = 0; While[Times @@ t == 0, k++; n = f[k]; If[n <= nn && t[[n]] == 0, t[[n]] = k]]; Join[{1}, t]
lk[n_]:=Module[{k=1},While[Mod[Prime[k],k]!=n,k++];k]; Array[lk,60,0] (* Harvey P. Dale, Nov 29 2013 *)

stop=110000; for(n=0,59,k=1; while(k

from sympy import prime, nextprime
def A073325(n):
    p, m = prime(n), n
    while p%m != n-1:
        p = nextprime(p)
        m += 1
    return m # Chai Wah Wu, Mar 18 2023

a(n) = Min{x; Mod[A000040(x), x]=n} = Min{x; A004648[x]=n}.

Definition revised by N. J. A. Sloane, Aug 12 2009

A216162 merged into this sequence by T. D. Noe, Sep 07 2012

A073326 Smallest x such that prime(x) == n (mod (x-pi(x)-1)).

Original entry on oeis.org

6, 67, 9, 10, 13, 96, 15, 16, 74, 73, 32, 85, 31, 4086, 228, 611, 28, 30, 44, 616, 263, 617, 43, 4090, 47, 633, 241, 631, 49, 122195143823, 48, 102, 123, 622, 62, 120, 65, 103, 112, 108, 64, 4094, 63, 127, 271, 109, 128, 129, 70, 132, 133, 137, 131, 4060, 644

Offset: 1

Labos Elemer, Jul 30 2002

nonn

			p(10) mod (10-PrimePi(10)-1) = 29 mod (10-4-1) = 29 mod 5 = 4 and a(4)=10.

Cf. A000040, A000720, A073324, A073326.

a[n_] := (k = 4; While[ Mod[ Prime[k], k - PrimePi[k] - 1] != n, k++ ]; k); Table[ a[n], {n, 1, 29}]

a(n) = Min{x : A000040(x) == n (mod (x-A000720(x)-1)) }.

Edited by Robert G. Wilson v, Jul 31 2002

a(30) from Giovanni Resta, Sep 02 2019

cp's OEIS Frontend

A072548 a(n) = sigma(n) mod PrimePi(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A073325 a(n) = least k > 0 such that prime(k) == n (mod k).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

Extensions

A073326 Smallest x such that prime(x) == n (mod (x-pi(x)-1)).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions