

A266475


Sum of the parts i_1 + i_2 + ... + i_{A001222(n)} of the unique strict partition with encoding n = Product_{j=1..A001222(n)} prime(i_jj+1).


3



0, 1, 2, 3, 3, 4, 4, 6, 5, 5, 5, 7, 6, 6, 6, 10, 7, 8, 8, 8, 7, 7, 9, 11, 7, 8, 9, 9, 10, 9, 11, 15, 8, 9, 8, 12, 12, 10, 9, 12, 13, 10, 14, 10, 10, 11, 15, 16, 9, 10, 10, 11, 16, 13, 9, 13, 11, 12, 17, 13, 18, 13, 11, 21, 10, 11, 19, 12, 12, 11, 20, 17, 21
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OFFSET

1,3


COMMENTS

A strict partition is a partition into distinct parts.


LINKS



FORMULA

[x^n] Sum_{i>=1} x^a(i) = A000009(n) for n>=0.


EXAMPLE

n = 12 = 2*2*3 = prime(1)*prime(1)*prime(2) encodes strict partition [1,2,4]. So a(12) = 1+2+4 = 7. Value a(n) = 7 occurs A000009(7) = 5 times, for n in {12, 17, 21, 22, 25}.


MAPLE

a:= n> ((l> add(l[j]+j1, j=1..nops(l)))(sort([seq(
numtheory[pi](i[1])$i[2], i=ifactors(n)[2])]))):
seq(a(n), n=1..100);


MATHEMATICA

a[n_] := Function[l, Sum[l[[j]]+j1, {j, 1, Length[l]}]][Sort[ Flatten[ Table[ Array[ PrimePi[i[[1]]]&, i[[2]]], {i, FactorInteger[n]}]]]];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



