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A359683
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Greatest positive integer whose reversed (weakly decreasing) prime indices have weighted sum (A318283) equal to n.
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11
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1, 2, 3, 5, 7, 11, 14, 22, 26, 34, 44, 55, 68, 85, 110, 130, 170, 190, 242, 290, 374, 418, 506, 638, 748, 836, 1012, 1276, 1364, 1628, 1914, 2090, 2552, 3190, 3410, 4070, 4510, 5060, 6380, 7018, 8140, 9020, 9922, 11396, 14036, 15004, 17908, 19844, 21692, 23452
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OFFSET
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0,2
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COMMENTS
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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 weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
2: {1}
3: {2}
5: {3}
7: {4}
11: {5}
14: {1,4}
22: {1,5}
26: {1,6}
34: {1,7}
44: {1,1,5}
55: {3,5}
68: {1,1,7}
85: {3,7}
110: {1,3,5}
130: {1,3,6}
170: {1,3,7}
190: {1,3,8}
242: {1,5,5}
290: {1,3,10}
The 6 numbers with weighted sum of reversed prime indices 9, together with their prime indices:
18: {1,2,2}
23: {9}
25: {3,3}
28: {1,1,4}
33: {2,5}
34: {1,7}
Hence a(9) = 34.
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MATHEMATICA
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nn=10;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
ots[y_]:=Sum[i*y[[i]], {i, Length[y]}];
seq=Table[ots[Reverse[primeMS[n]]], {n, 1, 2^nn}];
Table[Position[seq, k][[-1, 1]], {k, 0, nn}]
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CROSSREFS
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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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