cp's OEIS Frontend

A341521 Triangular array T(n,k) = A156552(A005940(1+n)*A005940(1+k)), read by rows, with n >= 0, 0 <= k <= n.

%I A341521 #11 Feb 20 2021 23:11:35
%S A341521 0,1,3,2,5,6,3,7,11,15,4,9,10,19,12,5,11,13,23,21,27,6,13,14,27,22,29,
%T A341521 30,7,15,23,31,39,47,55,63,8,17,18,35,20,37,38,71,24,9,19,21,39,25,43,
%U A341521 45,79,41,51,10,21,22,43,26,45,46,87,42,53,54,11,23,27,47,43,55,59,95,75,87,91,111,12,25,26,51,28,53,54,103,44,57,58,107,60
%N A341521 Triangular array T(n,k) = A156552(A005940(1+n)*A005940(1+k)), read by rows, with n >= 0, 0 <= k <= n.
%C A341521 A341520 is the main entry for this dyadic function. See comments there.
%H A341521 Antti Karttunen, <a href="/A341521/b341521.txt">Table of n, a(n) for n = 0..10439; the first 144 rows of the triangle</a>
%H A341521 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A341521 T(n,k) = A341520(n,k).
%e A341521 The triangle begins as:
%e A341521   0,
%e A341521   1,  3,
%e A341521   2,  5,  6,
%e A341521   3,  7, 11, 15,
%e A341521   4,  9, 10, 19, 12,
%e A341521   5, 11, 13, 23, 21, 27,
%e A341521   6, 13, 14, 27, 22, 29, 30,
%e A341521   7, 15, 23, 31, 39, 47, 55, 63,
%e A341521   8, 17, 18, 35, 20, 37, 38, 71, 24,
%e A341521   9, 19, 21, 39, 25, 43, 45, 79, 41, 51,
%e A341521 etc.
%o A341521 (PARI)
%o A341521 up_to = 104;
%o A341521 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A341521 A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A341521 A341520sq(n,k) = A156552(A005940(1+n)*A005940(1+k));
%o A341521 A341521list(up_to) = { my(v = vector(1+up_to), i=0); for(n=0,oo, for(k=0,n, i++; if(i > #v, return(v)); v[i] = A341520sq(n,k))); (v); };
%o A341521 v341521 = A341521list(up_to);
%o A341521 A341521(n) = v341521[1+n]; \\ _Antti Karttunen_, Feb 15 2021
%Y A341521 The lower triangular region of A341520 read by rows.
%Y A341521 Cf. A005940, A156552.
%Y A341521 Cf. A001477 (the left edge), A088698 (the right edge).
%K A341521 nonn,tabl,look
%O A341521 0,3
%A A341521 _Antti Karttunen_, Feb 15 2021