cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A143853 Primes p that divide the sum of their remainders modulo all smaller composites (=A233131(p)).

Original entry on oeis.org

2, 3, 23, 53, 613, 490537
Offset: 1

Views

Author

Neil Fernandez, Sep 03 2008

Keywords

Comments

The prime elements of A233344.

Examples

			Composites smaller than 23 are 4,6,8,9,10,12,14,15,16,18,20,21 and 22. 23 is congruent to 3,5,7,5,3,11,9,8,7,5,3 and 2 modulo these numbers respectively. The sum of these residues is 69. This is a multiple of 23, so 23 is in the sequence.

Crossrefs

Cf. A143851

Extensions

490537 from Max Alekseyev, Sep 15 2009
Term 2 prepended by Max Alekseyev, Dec 07 2013

A233131 Sum of remainders of n modulo all smaller composite numbers.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 4, 2, 5, 9, 14, 9, 15, 21, 28, 24, 33, 27, 37, 33, 44, 56, 69, 52, 66, 81, 88, 87, 105, 92, 111, 102, 122, 143, 165, 139, 163, 187, 212, 196, 223, 209, 237, 239, 244, 274, 305, 266, 298, 296, 330, 335, 371, 347, 384, 368, 407, 447, 488, 432, 474, 516, 529, 513, 558, 543, 590, 599, 647, 637, 687, 620
Offset: 0

Views

Author

Max Alekseyev, Dec 07 2013

Keywords

Crossrefs

Cf. A143853, A233344

Programs

  • Mathematica
    Table[Total[Mod[n,Select[Range[n-1],CompositeQ]]],{n,0,80}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 01 2018 *)

Formula

a(n) = A004125(n) - A024934(n).
Showing 1-2 of 2 results.

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