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A324738 Number of subsets of {1...n} containing no element > 1 whose prime indices all belong to the subset. 13
1, 2, 3, 5, 8, 13, 26, 42, 72, 120, 232, 376, 752, 1128, 2256, 4512, 8256, 13632, 27264, 42048, 82944, 158976, 313344, 497664, 995328, 1700352, 3350016, 5815296, 11630592, 17491968, 34983936, 56954880, 108933120, 210788352, 418258944, 804667392, 1609334784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..100

EXAMPLE

The a(0) = 1 through a(6) = 26 subsets:

  {}  {}   {}   {}     {}     {}       {}

      {1}  {1}  {1}    {1}    {1}      {1}

           {2}  {2}    {2}    {2}      {2}

                {3}    {3}    {3}      {3}

                {1,3}  {4}    {4}      {4}

                       {1,3}  {5}      {5}

                       {2,4}  {1,3}    {6}

                       {3,4}  {1,5}    {1,3}

                              {2,4}    {1,5}

                              {2,5}    {1,6}

                              {3,4}    {2,4}

                              {4,5}    {2,5}

                              {2,4,5}  {2,6}

                                       {3,4}

                                       {3,6}

                                       {4,5}

                                       {4,6}

                                       {5,6}

                                       {1,3,6}

                                       {1,5,6}

                                       {2,4,5}

                                       {2,4,6}

                                       {2,5,6}

                                       {3,4,6}

                                       {4,5,6}

                                       {2,4,5,6}

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {n, 0, 10}]

PROG

(PARI)

pset(n)={my(b=0, f=factor(n)[, 1]); sum(i=1, #f, 1<<(primepi(f[i])))}

a(n)={my(p=vector(n, k, if(k==1, 1, pset(k))), d=0); for(i=1, #p, d=bitor(d, p[i]));

((k, b)->if(k>#p, 1, my(t=self()(k+1, b)); if(bitnegimply(p[k], b), t+=if(bittest(d, k), self()(k+1, b+(1<<k)), t)); t))(1, 0)} \\ Andrew Howroyd, Aug 16 2019

CROSSREFS

The maximal case is A324744. The case of subsets of {2...n} is A324739. The strict integer partition version is A324749. The integer partition version is A324754. The Heinz number version is A324759. An infinite version is A324694.

Cf. A000720, A001221, A001462, A007097, A076078, A084422, A085945, A112798, A276625, A279861, A290689, A290822, A304360, A306844.

Cf. A324695, A324736, A324741, A324750, A324755, A324760.

Sequence in context: A125730 A074030 A024318 * A132915 A030036 A115212

Adjacent sequences:  A324735 A324736 A324737 * A324739 A324740 A324741

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 13 2019

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Aug 16 2019

STATUS

approved

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Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)