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

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, 30, 7, 15, 23, 31, 39, 47, 55, 63, 8, 17, 18, 35, 20, 37, 38, 71, 24, 9, 19, 21, 39, 25, 43, 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

Offset: 0

Author

Antti Karttunen, Feb 15 2021

Keywords

• nonn
• tabl
• look

Comments

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

Examples

			The triangle begins as:
  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, 30,
  7, 15, 23, 31, 39, 47, 55, 63,
  8, 17, 18, 35, 20, 37, 38, 71, 24,
  9, 19, 21, 39, 25, 43, 45, 79, 41, 51,
etc.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10439; the first 144 rows of the triangle
• Index entries for sequences related to binary expansion of n

Crossrefs

The lower triangular region of A341520 read by rows.

Cf. A005940, A156552.

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

Programs

PARI

up_to = 104;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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 };
A341520sq(n,k) = A156552(A005940(1+n)*A005940(1+k));
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); };
v341521 = A341521list(up_to);
A341521(n) = v341521[1+n]; \\ Antti Karttunen, Feb 15 2021

Formula

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