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 A318360 Number of set multipartitions (multisets of sets) of a multiset whose multiplicities are the prime indices of n. 23
 1, 1, 1, 2, 1, 2, 1, 5, 3, 2, 1, 6, 1, 2, 3, 15, 1, 9, 1, 6, 3, 2, 1, 21, 4, 2, 16, 6, 1, 10, 1, 52, 3, 2, 4, 35, 1, 2, 3, 22, 1, 10, 1, 6, 19, 2, 1, 83, 5, 13, 3, 6, 1, 66, 4, 22, 3, 2, 1, 41, 1, 2, 20, 203, 4, 10, 1, 6, 3, 14, 1, 153, 1, 2, 26, 6, 5, 10, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A050320(A181821(n)). From Andrew Howroyd, Dec 10 2018:(Start) a(p) = 1 for prime(p). a(prime(i)*prime(j)) = min(i,j) + 1. a(prime(n)^k) = A188392(n,k). (End) EXAMPLE The a(12) = 6 set multipartitions of {1,1,2,3}:   {{1},{1,2,3}}   {{1,2},{1,3}}   {{1},{1},{2,3}}   {{1},{2},{1,3}}   {{1},{3},{1,2}}   {{1},{1},{2},{3}} MATHEMATICA nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]]; sqfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sqfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ]}]]; Table[Length[sqfacs[Times@@Prime/@nrmptn[n]]], {n, 80}] PROG (PARI) permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} sig(n)={my(f=factor(n)); concat(vector(#f~, i, vector(f[i, 2], j, primepi(f[i, 1]))))} count(sig)={my(n=vecsum(sig), s=0); forpart(p=n, my(q=prod(i=1, #p, 1 + x^p[i] + O(x*x^n))); s+=prod(i=1, #sig, polcoef(q, sig[i]))*permcount(p)); s/n!} a(n)={if(n==1, 1, my(s=sig(n)); if(#s<=2, if(#s==1, 1, min(s[1], s[2])+1), count(sig(n))))} \\ Andrew Howroyd, Dec 10 2018 CROSSREFS Cf. A001055, A007716, A049311, A116540, A181821, A188392, A255906. Cf. A318283, A318284, A318286, A318361, A318362, A318369. Sequence in context: A146002 A109087 A102048 * A102551 A217437 A152823 Adjacent sequences:  A318357 A318358 A318359 * A318361 A318362 A318363 KEYWORD nonn AUTHOR Gus Wiseman, Aug 24 2018 STATUS approved

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Last modified April 22 06:14 EDT 2019. Contains 322329 sequences. (Running on oeis4.)