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A359683
Greatest positive integer whose reversed (weakly decreasing) prime indices have weighted sum (A318283) equal to n.
11
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
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.
The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
First position of n in A318283, unreversed A304818.
The unreversed version is A359497.
The least instead of greatest is A359679, unreversed A359682.
A112798 lists prime indices, length A001222, sum A056239.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Sequence in context: A027341 A363230 A262371 * A184642 A350836 A094252
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2023
EXTENSIONS
More terms from Jinyuan Wang, Jan 26 2023
STATUS
approved