A115862 Triangle where a(1,1)=0; a(n,m) is number of terms among the first (n-1) terms of A115863 that are not coprime to m. A115863(n) is the sum of the terms of the n-th row of A115862.

0, 0, 1, 0, 1, 1, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 3, 2, 0, 2, 2, 2, 2, 3, 2, 2, 0, 2, 3, 2, 3, 4, 2, 2, 3, 0, 2, 4, 2, 3, 5, 3, 2, 4, 4, 0, 2, 4, 2, 3, 5, 3, 2, 4, 4, 1, 0, 3, 5, 3, 4, 6, 3, 3, 5, 5, 1, 6, 0, 4, 5, 4, 4, 7, 3, 4, 5, 6, 2, 7, 2

Offset

1,8

Comments

If a(1,1) were instead 1, then row 2 would be [0,0] and the rest of the triangle would be the same as when a(1,1) = 0. For our purposes, 0 is considered to be coprime only with 1.

Links

Table of n, a(n) for n=1..91.

Example

The first 5 terms of A115863 are 0,1,2,5 and 7. Among these terms 0 are not coprime with 1, 2 are not coprime with 2, 1 is not coprime with 3, 2 are not coprime with 4, 2 are not coprime with 5 and 2 are not coprime with 6.
So row 6 of the triangle is [0,2,1,2,2,2].
(And so A115863(6) = 0 + 2 + 1 + 2 + 2 + 2 = 9.)
Triangle begins:
  0,
  0, 1,
  0, 1, 1,
  0, 2, 1, 2,
  0, 2, 1, 2, 2,
  0, 2, 1, 2, 2, 2,
  0, 2, 2, 2, 2, 3, 2,
  0, 2, 2, 2, 2, 3, 2, 2,
  ...

Prog

(PARI)  tabl(nn) = {my(row = vector(1), v = vector(nn)); row[1] = 0; print(row); for (n=1, nn, v[n] = vecsum(row); row = vector(n+1, k, #select(x->(gcd(x, k)!=1), vector(n, k, v[k]))); print(row); ); } \\ Michel Marcus, Sep 06 2019

Crossrefs

Cf. A115863, A115758.

Sequence in context: A229951 A165034 A193347 * A296030 A270144 A255980

Adjacent sequences: A115859 A115860 A115861 * A115863 A115864 A115865

Keyword

nonn,tabl

Author

Leroy Quet, Feb 01 2006

Extensions

More terms from Michel Marcus, Sep 06 2019

Status

approved