cp's OEIS Frontend

A359755 Positions of first appearances in the sequence of weighted sums of prime indices (A304818).

%I A359755 #6 Jan 16 2023 11:15:03
%S A359755 1,2,3,4,6,7,8,10,12,15,16,18,20,24,26,28,36,40,46,48,50,52,56,62,68,
%T A359755 74,76,86,88,92,94,106,107,118,122,124,131,134,136,142,146,152,158,
%U A359755 164,166,173,178,188,193,194,199,202,206,214,218,226,229,236,239,254
%N A359755 Positions of first appearances in the sequence of weighted sums of prime indices (A304818).
%C A359755 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 A359755 The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
%e A359755 The terms together with their prime indices begin:
%e A359755     1: {}
%e A359755     2: {1}
%e A359755     3: {2}
%e A359755     4: {1,1}
%e A359755     6: {1,2}
%e A359755     7: {4}
%e A359755     8: {1,1,1}
%e A359755    10: {1,3}
%e A359755    12: {1,1,2}
%e A359755    15: {2,3}
%e A359755    16: {1,1,1,1}
%e A359755    18: {1,2,2}
%e A359755    20: {1,1,3}
%e A359755    24: {1,1,1,2}
%t A359755 nn=1000;
%t A359755 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A359755 ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
%t A359755 seq=Table[ots[primeMS[n]],{n,1,nn}];
%t A359755 Select[Range[nn],FreeQ[seq[[Range[#-1]]],seq[[#]]]&]
%Y A359755 The version for standard compositions is A089633, zero-based A359756.
%Y A359755 Positions of first appearances in A304818, reverse A318283.
%Y A359755 The zero-based version is A359675, unsorted A359676.
%Y A359755 The reverse zero-based version is A359680, unsorted A359681.
%Y A359755 This is the sorted version of A359682, reverse A359679.
%Y A359755 The reverse version is A359754.
%Y A359755 A053632 counts compositions by weighted sum.
%Y A359755 A112798 lists prime indices, length A001222, sum A056239.
%Y A359755 A320387 counts multisets by weighted sum, zero-based A359678.
%Y A359755 A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
%Y A359755 Cf. A029931, A124757, A243055, A358194, A359497, A359674, A359683.
%K A359755 nonn
%O A359755 1,2
%A A359755 _Gus Wiseman_, Jan 15 2023