A359679 - OEIS

%I #7 Jan 15 2023 09:51:20

%S 1,2,3,4,6,10,8,12,19,18,16,24,27,36,43,32,48,59,61,67,71,64,79,83,89,

%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,

%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269

%N Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n.

%C 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.

%C The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.

%e 12 has reversed prime indices (2,1,1), with weighted sum 7, and no number < 12 has the same weighted sum of reversed prime indices, so a(7) = 12.

%t nn=20;

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];

%t seq=Table[ots[Reverse[primeMS[n]]],{n,1,Prime[nn]^2}];

%t Table[Position[seq,k][[1,1]],{k,0,nn}]

%Y The version for standard compositions is A089633, zero-based A359756.

%Y First position of n in A318283, unreversed A304818.

%Y The unreversed zero-based version is A359676.

%Y The sorted zero-based version is A359680, unreversed A359675.

%Y The zero-based version is A359681.

%Y The unreversed version is A359682.

%Y The greatest instead of least is A359683, unreversed A359497.

%Y The sorted version is A359754, unreversed A359755.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A320387 counts multisets by weighted sum, zero-based A359678.

%Y A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.

%Y Cf. A001248, A029931, A053632, A055932, A231204, A243055, A359043, A358194, A359360, A359677.

%K nonn

%O 0,2

%A _Gus Wiseman_, Jan 14 2023