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A186973 Number of subsets of {1, 2, ..., n} containing n and having pairwise coprime elements; also row sums of A186972. 4
1, 2, 4, 4, 12, 4, 28, 16, 32, 12, 116, 16, 248, 48, 72, 112, 728, 64, 1520, 192, 384, 256, 3872, 256, 3168, 736, 2752, 832, 15488, 256, 31232, 7424, 6272, 4096, 9600, 1792, 91648, 9344, 16000, 5632, 214272, 3072, 431616, 37376, 38912, 43008, 982528 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..220

EXAMPLE

a(6) = 4 because there are 4 subsets of {1,2,3,4,5,6} containing 6 and having pairwise coprime elements: {6}, {1,6}, {5,6}, {1,5,6}.

MAPLE

with(numtheory):

s:= proc(m, r) option remember; mul(`if`(i<r, i, 1), i=factorset(m)) end:

g:= proc(n) option remember; `if`(n<4, n, pi(n)-nops(factorset(n))+2) end:

h:= n-> mul(ilog[j](n), j={ithprime(i)$i=1..pi(n)} minus factorset(n)):

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

         end; c

      fi

    end:

a:= n-> h(n) + add(b(s(n, n), n, k), k=1..g(n)-1):

seq(a(n), n=1..50);

MATHEMATICA

s[m_, r_] := s[m, r] = Product[If[i<r, i, 1], {i, FactorInteger[m][[All, 1]]}]; a[n_] := a[n] = If[n<4, n, PrimePi[n]-Length[FactorInteger[n]]+2]; 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]; Table[Sum[t[n, k], {k, 1, a[n]}], {n, 1, 50}] (* Jean-Fran├žois Alcover, Dec 04 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A186971, A186972, A186994. Rightmost elements in rows of triangle A186975.

Sequence in context: A186991 A186992 A186993 * A225232 A319210 A292303

Adjacent sequences:  A186970 A186971 A186972 * A186974 A186975 A186976

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 01 2011

STATUS

approved

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Last modified December 14 15:01 EST 2019. Contains 329979 sequences. (Running on oeis4.)