%I #19 Apr 12 2024 17:42:53

%S 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,

%T 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,

%U 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

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

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

%H G. C. Greubel, <a href="/A174947/b174947.txt">Rows n = 1..50 of the triangle, flattened</a>

%e Triangle begins

%e 1;

%e 0, 1;

%e 0, 0, 1;

%e 0, 2, 3, 1;

%e 0, 0, 2, 5, 1;

%e 0, 2, 4, 0, 3, 1;

%e 0, 0, 3, 4, 7, 5, 1;

%e 0, 2, 0, 6, 9, 7, 3, 1;

%e 0, 0, 4, 3, 2, 11, 7, 5, 1;

%e 0, 0, 0, 2, 8, 4, 13, 11, 7, 1;

%t Table[Mod[1+Prime[n], Prime[k]], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 10 2024 *)

%o (PARI) trga(nrows) = {for (n=1, nrows, for (k=1, n, print1(sigma(prime(n)) % prime(k), ", ");); print(););} \\ _Michel Marcus_, Apr 11 2013

%o (Magma)

%o [(1+NthPrime(n)) mod NthPrime(k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 10 2024

%o (SageMath)

%o 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

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

%K nonn,tabl

%O 1,8

%A _Juri-Stepan Gerasimov_, Dec 02 2010

%E Corrected by _D. S. McNeil_, Dec 02 2010