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A359757
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Greatest positive integer whose weakly increasing prime indices have zero-based weighted sum (A359674) equal to n.
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2
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4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 12167, 11449, 15341, 24389, 16399, 26071, 29791, 31117, 35557, 50653, 39401, 56129, 68921, 58867, 72283, 83521, 79007, 86903, 103823
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OFFSET
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1,1
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COMMENTS
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Appears to first differ from A001248 at a(27) = 12167, A001248(27) = 10609.
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.
The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
4: {1,1}
9: {2,2}
25: {3,3}
49: {4,4}
121: {5,5}
169: {6,6}
289: {7,7}
361: {8,8}
529: {9,9}
841: {10,10}
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MATHEMATICA
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nn=10;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]], {i, Length[y]}];
seq=Table[wts[prix[n]], {n, 2^nn}];
Table[Position[seq, k][[-1, 1]], {k, nn}]
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PROG
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(PARI) a(n)={ my(recurse(r, k, m) = if(k==1, if(m>=r, prime(r)^2),
my(z=0); for(j=1, min(m, (r-k*(k-1)/2)\k), z=max(z, self()(r-k*j, k-1, j)*prime(j))); z));
vecmax(vector((sqrtint(8*n+1)-1)\2, k, recurse(n, k, n)));
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CROSSREFS
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A053632 counts compositions by zero-based weighted sum.
A124757 = zero-based weighted sum of standard compositions, reverse A231204.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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