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Row sums of triangle A156837
3

%I #9 Nov 30 2024 16:45:38

%S 1,3,3,7,3,13,3,17,11,17,3,51,3,21,37,55,3,83,3,113,63,29,3,271,75,33,

%T 103,223,3,453,3,329,139,41,427,897,3,45,189,1265,3,1267,3,651,1277,

%U 53,3,2943,929,1571,313,1001,3,3147,2009,4843,387,65,3,9159,3,69,6541,5459,3647,6753,3,2053,559,15299,3,25677,3,81

%N Row sums of triangle A156837

%C a(n) = 3 iff n is prime.

%H Antti Karttunen, <a href="/A156838/b156838.txt">Table of n, a(n) for n = 1..10000</a>

%F Row sums of triangle A156837.

%e a(4) = 7 since row 4 of triangle A156837 = (3, 3, 0, 1).

%p A156838 := proc(n)

%p add(A156837(n,k),k=1..n) ;

%p end proc: # _R. J. Mathar_, Mar 03 2013

%o (PARI)

%o A156348(n, k) = if(k<1 || k>n || n%k, 0, binomial(n/k-2+k, k-1)); \\ After _R. J. Mathar_'s Maple-program in A156348

%o A156837(n, k) = sum(j=k,n,if(n%j, 0, A156348(j, k)));

%o A156838(n) = sumdiv(n,d,A156837(n,d)); \\ _Antti Karttunen_, Nov 30 2024

%Y A156837

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_ & _Mats Granvik_, Feb 16 2009

%E Extended beyond a(14) by _R. J. Mathar_, Mar 03 2013

%E More terms from _Antti Karttunen_, Nov 30 2024