The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A186974 Irregular triangle T(n,k), n>=1, 1<=k<=A036234(n), read by rows: T(n,k) is the number of k-element subsets of {1, 2, ..., n} having pairwise coprime elements. 20
 1, 2, 1, 3, 3, 1, 4, 5, 2, 5, 9, 7, 2, 6, 11, 8, 2, 7, 17, 19, 10, 2, 8, 21, 25, 14, 3, 9, 27, 37, 24, 6, 10, 31, 42, 26, 6, 11, 41, 73, 68, 32, 6, 12, 45, 79, 72, 33, 6, 13, 57, 124, 151, 105, 39, 6, 14, 63, 138, 167, 114, 41, 6, 15, 71, 159, 192, 128, 44, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,k) = 0 for k > A036234(n). The triangle contains all positive values of T. LINKS Alois P. Heinz, Rows n = 1..220, flattened FORMULA T(n,k) = Sum_{i=1..n} A186972(i,k). EXAMPLE T(5,3) = 7 because there are 7 3-element subsets of {1,2,3,4,5} having pairwise coprime elements: {1,2,3}, {1,2,5}, {1,3,4}, {1,3,5}, {1,4,5}, {2,3,5}, {3,4,5}. Irregular Triangle T(n,k) begins:   1;   2,  1;   3,  3,  1;   4,  5,  2;   5,  9,  7,  2;   6, 11,  8,  2;   7, 17, 19, 10, 2; MAPLE with(numtheory): s:= proc(m, r) option remember; mul(`if`(i pi(n) +1: b:= proc(t, n, k) option remember; local c, d, h;       if k=0 or k>n then 0     elif k=1 then 1     elif k=2 and t=n then `if`(n<2, 0, phi(n))     else c:= 0;          d:= 2-irem(t, 2);          for h from 1 to n-1 by d do            if igcd(t, h)=1 then c:= c +b(s(t*h, h), h, k-1) fi          od; c       fi     end: T:= proc(n, k) option remember;        b(s(n, n), n, k) +`if`(n<2, 0, T(n-1, k))     end: seq(seq(T(n, k), k=1..a(n)), n=1..20); MATHEMATICA s[m_, r_] := s[m, r] = Product[If[i < r, i, 1], {i, FactorInteger[m][[All, 1]]}]; a[n_] := PrimePi[n]+1; b[t_, n_, k_] := b[t, n, k] = Module[{c, d, h}, Which[k == 0 || k > n, 0, k == 1, 1, k == 2 && t == n, If[n < 2, 0, EulerPhi[n]], True, c = 0; d = 2-Mod[t, 2]; For[h = 1, h <= n-1, h = h+d, If[ GCD[t, h] == 1, c = c + b[s[t*h, h], h, k-1]]]; c]]; t[n_, k_] := t[n, k] = b[s[n, n], n, k] + If[n < 2, 0, t[n-1, k]]; Table[Table[t[n, k], { k, 1, a[n]}], {n, 1, 20}] // Flatten (* Jean-François Alcover, Dec 17 2013, translated from Maple *) CROSSREFS Columns k=1-10 give: A000027, A015614, A015617, A015623, A015698, A186982, A186983, A186984, A186985, A186986. Row sums give A187106. Rightmost terms of rows give A319187. Cf. A036234, A186972. Sequence in context: A183110 A117895 A188002 * A286312 A278492 A128139 Adjacent sequences:  A186971 A186972 A186973 * A186975 A186976 A186977 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Mar 02 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 27 18:56 EDT 2021. Contains 347694 sequences. (Running on oeis4.)