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A139553 Triangle read by rows: T(n,k) = if n>=4*k and n<4*k*A014963(k) then k else 1; T(n,0)=1.

%I A139553 #9 Jan 03 2019 13:29:36
%S A139553 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A139553 1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,
%U A139553 2,1,1,1,1,1,1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,1,1
%N A139553 Triangle read by rows: T(n,k) = if n>=4*k and n<4*k*A014963(k) then k else 1; T(n,0)=1.
%C A139553 Row products give A139554.
%H A139553 Antti Karttunen, <a href="/A139553/b139553.txt">Table of n, a(n) for n = 0..23219; the first 215 rows of triangle</a>
%e A139553 Row products of the triangle are:
%e A139553 1 = 1
%e A139553 1*1 = 1
%e A139553 1*1*1 = 1
%e A139553 1*1*1*1 = 1
%e A139553 1*1*1*1*1 = 1
%e A139553 1*1*1*1*1*1 = 1
%e A139553 1*1*1*1*1*1*1 = 1
%e A139553 1*1*1*1*1*1*1*1 = 1
%e A139553 1*1*2*1*1*1*1*1*1 = 2
%o A139553 (Excel) =if(and(row()-1>=(column()-1)*4;row()-1 < A014963(k-1)*(column()-1)*4);column()-1;1)
%o A139553 (PARI)
%o A139553 up_to = 23220; \\ binomial(215+1,2)
%o A139553 A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); }; \\ From A014963 by _Charles R Greathouse IV_, Jun 10 2011
%o A139553 A139553tr(n, k) = if(0==k,1,if((n>=(4*k))&&(n<(4*k*A014963(k))),k,1));
%o A139553 A139553list(up_to) = { my(v = vector(up_to), i=0); for(n=1,oo, for(k=1,n, i++; if(i > up_to, return(v)); v[i] = A139553tr(n-1,k-1))); (v); };
%o A139553 v139553 = A139553list(up_to);
%o A139553 A139553(n) = v139553[1+n]; \\ _Antti Karttunen_, Jan 03 2019
%Y A139553 Cf. A139554, A139547, A003418.
%K A139553 nonn,tabl
%O A139553 0,39
%A A139553 _Mats Granvik_, Apr 27 2008
%E A139553 Typo in the definition corrected by _Antti Karttunen_, Jan 03 2019