A095167 -id:A095167 - cp's OEIS frontend

A095169 Leading diagonal of the triangle A095167.

1, 4, 9, 14, 30, 26, 63, 48, 66, 72, 176, 90, 247, 119, 144, 168, 425, 198, 551, 230, 270, 290, 828, 327, 445, 394, 474, 470, 1305, 519, 1426, 592, 636, 680, 749, 756, 2072, 838, 903, 926, 2624, 978, 2881, 1058, 1130, 1194, 3337, 1266, 1582, 1356

Offset: 1

Amarnath Murthy, Jun 01 2004

nonn

Cf. A095167, A095168, A095170, A095171.

S=Set(); for(n=2,20, k=0; m=1; while(k1, S=setunion(S,[m]); k++) ); print1(" ",m) ) (Alekseyev)

More terms from Max Alekseyev, Jun 30 2005

A095170 Row sums of A095167.

Original entry on oeis.org

1, 6, 18, 44, 95, 127, 280, 318, 432, 616, 1276, 962, 2067, 1480, 1820, 2360, 4709, 3258, 6802, 4105, 4943, 5818, 12719, 7345, 9235, 9398, 11373, 11675, 25201, 14899, 28458, 17828, 18882, 21879, 23246, 25703, 50283, 30272, 31983, 35175, 71668

Offset: 1

Amarnath Murthy, Jun 01 2004

nonn

Cf. A095167, A095168, A095169, A095171.

S=Set();for(n=2,50,k=0;m=1;s=0;while(k1,S=setunion(S,[m]);k++;s+=m));print1(" ",s)) (Alekseyev)

More terms from Max Alekseyev, Jun 30 2005

A095171 Number of multiples of n in the n-th row of the triangle A095167.

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 7, 3, 3, 2, 11, 1, 13, 2, 2, 2, 17, 2, 19, 2, 2, 2, 23, 1, 4, 2, 2, 1, 29, 2, 31, 2, 3, 2, 3, 2, 37, 3, 3, 2, 41, 1, 43, 2, 3, 1, 47, 2, 8, 2, 2, 1, 53, 1, 4, 2, 3, 3, 59, 2, 61, 2, 3, 3, 3, 1, 67, 2, 2, 2, 71, 1, 73, 3, 2, 1, 3, 1, 79, 1, 3, 2, 83, 1, 4, 2, 1, 3, 89, 1, 5, 1, 3, 2, 3, 2

Offset: 1

Amarnath Murthy, Jun 01 2004

nonn

a(p) = p if p is a prime. a(4) = 2 as among 8, 10,12,14, there are two multiples of 4.

Cf. A095167, A095168, A095169, A095170.

S=Set();for(n=2,100,k=0;m=1;s=0;while(k1,S=setunion(S,[m]);k++;if(m%n==0,s++)));print1(" ",s)) (Alekseyev)

More terms from Max Alekseyev, Jun 30 2005

A081964 In the following triangle the n-th row contains n numbers relatively prime to n and not occurring in a previous row. a(1) = 1. Sequence contains the triangle by rows.

Original entry on oeis.org

1, 3, 5, 2, 4, 7, 9, 11, 13, 15, 6, 8, 12, 14, 16, 17, 19, 23, 25, 29, 31, 10, 18, 20, 22, 24, 26, 27, 21, 33, 35, 37, 39, 41, 43, 45, 28, 32, 34, 38, 40, 44, 46, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 30, 36, 42, 48, 50, 52, 54, 56, 58, 60, 62, 55, 65, 77, 79, 83, 85

Offset: 1

Amarnath Murthy, Apr 03 2003

			Triangle begins:
1
3 5
2 4 7
9 11 13 15
6 8 12 14 16
...

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, Perl program for this sequence

Cf. A081965, A081966.

Cf. A095167 (noncoprime instead of coprime).

Perl
```
See Link section.
```

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 08 2003

A076034 Group the natural numbers so that the n-th group contains the smallest set of n relatively prime numbers: (1), (2, 3), (4, 5, 7), (6, 11, 13, 17), (8, 9, 19, 23, 25), (10, 21, 29, 31, 37, 41), ...

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 13, 17, 8, 9, 19, 23, 25, 10, 21, 29, 31, 37, 41, 12, 35, 43, 47, 53, 59, 61, 14, 15, 67, 71, 73, 79, 83, 89, 16, 27, 49, 55, 97, 101, 103, 107, 109, 18, 65, 77, 113, 127, 131, 137, 139, 149, 151, 20, 33, 91, 157, 163, 167, 173, 179, 181, 191, 193

Offset: 1

Amarnath Murthy, Oct 01 2002

			The triangle begins:
   1;
   2, 3;
   4,  5,  7;
   6, 11, 13, 17;
   8,  9, 19, 23, 25;
  10, 21, 29, 31, 37, 41;
  ...

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, PERL program for this sequence

Cf. A075383, A076032, A076033, A095167.

S:=[$1..1000]: Res:= NULL:
for n from 1 to 20 do
  A:= [S[1]]; R:= 1; count:= 1;
  for k from 2 while count < n do
    if andmap(t -> igcd(t,S[k])=1, A) then count:= count+1; A:= [op(A),S[k]]; R:= R,k; fi
  od;
  S:= subsop(op(map(t -> t=NULL, [R])),S);
  Res:= Res, op(A);
od:
Res; # Robert Israel, Dec 04 2022

Perl
```
# See Links section.
```

More terms from David Wasserman, Jan 29 2005

Crossrefs added by Paul Tek, Oct 24 2015

A095168 Leading diagonal of A095169.

Original entry on oeis.org

1, 2, 3, 8, 5, 16, 7, 32, 27, 50, 11, 69, 13, 92, 85, 122, 17, 147, 19, 145, 161, 232, 23, 273, 235, 328, 333, 287, 29, 472, 31, 520, 407, 595, 497, 639, 37, 758, 533, 755, 41, 763, 43, 649, 955, 1064, 47, 1137, 1043, 1135

Offset: 1

Amarnath Murthy, Jun 01 2004

nonn

Cf. A095167, A095169, A095170, A095171.

S=Set();for(n=2,50,k=0;m=1;while(k1,S=setunion(S,[m]);if(k==0,print1(" ",m));k++))) (Alekseyev)

More terms from Max Alekseyev, Jun 30 2005

cp's OEIS Frontend

A095169 Leading diagonal of the triangle A095167.

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A095170 Row sums of A095167.

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A095171 Number of multiples of n in the n-th row of the triangle A095167.

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A081964 In the following triangle the n-th row contains n numbers relatively prime to n and not occurring in a previous row. a(1) = 1. Sequence contains the triangle by rows.

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A076034 Group the natural numbers so that the n-th group contains the smallest set of n relatively prime numbers: (1), (2, 3), (4, 5, 7), (6, 11, 13, 17), (8, 9, 19, 23, 25), (10, 21, 29, 31, 37, 41), ...

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Maple

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A095168 Leading diagonal of A095169.

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