A341521 - OEIS

%I #11 Feb 20 2021 23:11:35

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

%C A341520 is the main entry for this dyadic function. See comments there.

%H 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 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F T(n,k) = A341520(n,k).

%e The triangle begins as:

%e   0,

%e   1,  3,

%e   2,  5,  6,

%e   3,  7, 11, 15,

%e   4,  9, 10, 19, 12,

%e   5, 11, 13, 23, 21, 27,

%e   6, 13, 14, 27, 22, 29, 30,

%e   7, 15, 23, 31, 39, 47, 55, 63,

%e   8, 17, 18, 35, 20, 37, 38, 71, 24,

%e   9, 19, 21, 39, 25, 43, 45, 79, 41, 51,

%e etc.

%o (PARI)

%o up_to = 104;

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o 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 A341520sq(n,k) = A156552(A005940(1+n)*A005940(1+k));

%o 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 v341521 = A341521list(up_to);

%o A341521(n) = v341521[1+n]; \\ _Antti Karttunen_, Feb 15 2021

%Y The lower triangular region of A341520 read by rows.

%Y Cf. A005940, A156552.

%Y Cf. A001477 (the left edge), A088698 (the right edge).

%K nonn,tabl,look

%O 0,3

%A _Antti Karttunen_, Feb 15 2021