A174947 Triangle read by rows: T(n,k) = (prime(n)+1) mod prime(k).

1, 0, 1, 0, 0, 1, 0, 2, 3, 1, 0, 0, 2, 5, 1, 0, 2, 4, 0, 3, 1, 0, 0, 3, 4, 7, 5, 1, 0, 2, 0, 6, 9, 7, 3, 1, 0, 0, 4, 3, 2, 11, 7, 5, 1, 0, 0, 0, 2, 8, 4, 13, 11, 7, 1, 0, 2, 2, 4, 10, 6, 15, 13, 9, 3, 1, 0, 2, 3, 3, 5, 12, 4, 0, 15, 9, 7, 1, 0, 0, 2, 0, 9, 3, 8, 4, 19, 13, 11, 5, 1, 0, 2, 4, 2, 0, 5, 10, 6, 21, 15, 13, 7, 3, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 02 2010

Keywords

• nonn
• tabl

Comments

Triangle read by rows: T(n,k) = Sigma(prime(n)) mod prime(k), where Sigma(prime(.)) is the sum of divisors of prime.

Examples

			Triangle begins
  1;
  0, 1;
  0, 0, 1;
  0, 2, 3, 1;
  0, 0, 2, 5, 1;
  0, 2, 4, 0, 3,  1;
  0, 0, 3, 4, 7,  5,  1;
  0, 2, 0, 6, 9,  7,  3,  1;
  0, 0, 4, 3, 2, 11,  7,  5, 1;
  0, 0, 0, 2, 8,  4, 13, 11, 7, 1;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A174428, A173655, A173662, A174996, A175620, A177226.

Programs

Magma

[(1+NthPrime(n)) mod NthPrime(k): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 10 2024

Mathematica

Table[Mod[1+Prime[n], Prime[k]], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Apr 10 2024 *)

PARI

trga(nrows) = {for (n=1, nrows, for (k=1, n, print1(sigma(prime(n)) % prime(k), ", ");); print(););} \\ Michel Marcus, Apr 11 2013

SageMath

flatten([[(1+nth_prime(n))%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 10 2024

Extensions

Corrected by D. S. McNeil, Dec 02 2010