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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 21:08 EST 2022. Contains 350565 sequences. (Running on oeis4.)