A341511 Triangular array T(n,k) = A005940(1+A156552(n)+A156552(k)), read by rows, with n >= 1, 1 <= k <= n.

1, 2, 3, 3, 4, 5, 4, 5, 6, 9, 5, 6, 9, 8, 7, 6, 9, 8, 7, 10, 15, 7, 10, 15, 12, 25, 18, 11, 8, 7, 10, 15, 12, 25, 16, 27, 9, 8, 7, 10, 15, 12, 27, 18, 25, 10, 15, 12, 25, 18, 27, 14, 11, 16, 21, 11, 14, 21, 20, 35, 30, 49, 24, 45, 50, 13, 12, 25, 18, 27, 16, 11, 20, 21, 14, 35, 36, 45, 13, 22, 33, 28, 55, 42, 77, 40, 63, 70, 121, 60, 17

Offset: 1

Author

Antti Karttunen, Feb 15 2021

Keywords

• nonn
• tabl

Comments

A341510 is the main entry for this dyadic function. See comments there.

Examples

			The triangle begins as:
  1,
  2,  3,
  3,  4,  5,
  4,  5,  6,  9,
  5,  6,  9,  8,  7,
  6,  9,  8,  7, 10, 15,
  7, 10, 15, 12, 25, 18, 11,
  8,  7, 10, 15, 12, 25, 16, 27,
  9,  8,  7, 10, 15, 12, 27, 18, 25,
etc.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 rows of the triangle
• Index entries for sequences computed from indices in prime factorization

Crossrefs

The lower triangular region of A341510 read by rows.

Cf. A005940, A156552.

Cf. A000027 (the left edge), A003961 (the right edge).

Programs

PARI

up_to = 105;
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 };
A341510sq(n,k) = A005940(1+A156552(n)+A156552(k));
A341511list(up_to) = { my(v = vector(up_to), i=0); for(n=1,oo, for(k=1,n, i++; if(i > #v, return(v)); v[i] = A341510sq(n,k))); (v); };
v341511 = A341511list(up_to);
A341511(n) = v341511[n];

Formula

T(n, k) = A341510(n, k).