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

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, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 0

Author

Gus Wiseman, Jan 14 2023

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

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

First position of n in A318283, unreversed A304818.

The unreversed zero-based version is A359676.

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

The zero-based version is A359681.

The unreversed version is A359682.

The greatest instead of least is A359683, unreversed A359497.

The sorted version is A359754, unreversed A359755.

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.

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

Programs

Mathematica

nn=20;
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,Prime[nn]^2}];
Table[Position[seq,k][[1,1]],{k,0,nn}]