cp's OEIS Frontend

A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674).

%I A359676 #6 Jan 15 2023 09:51:05
%S A359676 1,4,6,8,14,12,16,20,30,24,32,36,40,52,48,56,100,72,80,92,96,104,112,
%T A359676 124,136,148,176,152,214,172,184,188,262,212,272,236,248,244,304,268,
%U A359676 346,284,328,292,386,316,398,332,376,356,458,388,478,404,472,412,526
%N A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674).
%C A359676 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 A359676 The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.
%e A359676 The terms together with their prime indices begin:
%e A359676     1: {}
%e A359676     4: {1,1}
%e A359676     6: {1,2}
%e A359676     8: {1,1,1}
%e A359676    14: {1,4}
%e A359676    12: {1,1,2}
%e A359676    16: {1,1,1,1}
%e A359676    20: {1,1,3}
%e A359676    30: {1,2,3}
%e A359676    24: {1,1,1,2}
%e A359676    32: {1,1,1,1,1}
%e A359676    36: {1,1,2,2}
%e A359676    40: {1,1,1,3}
%e A359676    52: {1,1,6}
%e A359676    48: {1,1,1,1,2}
%t A359676 nn=20;
%t A359676 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A359676 wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
%t A359676 seq=Table[wts[primeMS[n]],{n,1,Prime[nn]^2}];
%t A359676 Table[Position[seq,k][[1,1]],{k,0,nn}]
%Y A359676 First position of n in A359674, reverse A359677.
%Y A359676 The sorted version is A359675, reverse A359680.
%Y A359676 The reverse one-based version is A359679, sorted A359754.
%Y A359676 The reverse version is A359681.
%Y A359676 The one-based version is A359682, sorted A359755.
%Y A359676 The version for standard compositions is A359756, one-based A089633.
%Y A359676 A053632 counts compositions by zero-based weighted sum.
%Y A359676 A112798 lists prime indices, length A001222, sum A056239.
%Y A359676 A124757 gives zero-based weighted sum of standard compositions, rev A231204.
%Y A359676 A304818 gives weighted sums of prime indices, reverse A318283.
%Y A359676 A320387 counts multisets by weighted sum, zero-based A359678.
%Y A359676 A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
%Y A359676 Cf. A001248, A029931, A055932, A243055, A359043, A358194, A359497, A359683.
%K A359676 nonn,look
%O A359676 1,2
%A A359676 _Gus Wiseman_, Jan 14 2023