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

1,2

Comments

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

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

Formula

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

Example

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.

Prog

(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];

Crossrefs

The lower triangular region of A341510 read by rows.

Cf. A005940, A156552.

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

Sequence in context: A361261 A120244 A094727 * A089308 A305579 A321440

Adjacent sequences: A341508 A341509 A341510 * A341512 A341513 A341514

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 15 2021

Status

approved