cp's OEIS Frontend

A359679 Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n.

%I A359679 #7 Jan 15 2023 09:51:20
%S A359679 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 A359679 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U A359679 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N A359679 Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n.
%C A359679 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 A359679 The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
%e A359679 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 A359679 nn=20;
%t A359679 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A359679 ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
%t A359679 seq=Table[ots[Reverse[primeMS[n]]],{n,1,Prime[nn]^2}];
%t A359679 Table[Position[seq,k][[1,1]],{k,0,nn}]
%Y A359679 The version for standard compositions is A089633, zero-based A359756.
%Y A359679 First position of n in A318283, unreversed A304818.
%Y A359679 The unreversed zero-based version is A359676.
%Y A359679 The sorted zero-based version is A359680, unreversed A359675.
%Y A359679 The zero-based version is A359681.
%Y A359679 The unreversed version is A359682.
%Y A359679 The greatest instead of least is A359683, unreversed A359497.
%Y A359679 The sorted version is A359754, unreversed A359755.
%Y A359679 A112798 lists prime indices, length A001222, sum A056239.
%Y A359679 A320387 counts multisets by weighted sum, zero-based A359678.
%Y A359679 A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
%Y A359679 Cf. A001248, A029931, A053632, A055932, A231204, A243055, A359043, A358194, A359360, A359677.
%K A359679 nonn
%O A359679 0,2
%A A359679 _Gus Wiseman_, Jan 14 2023