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A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674). 14
1, 4, 6, 8, 14, 12, 16, 20, 30, 24, 32, 36, 40, 52, 48, 56, 100, 72, 80, 92, 96, 104, 112, 124, 136, 148, 176, 152, 214, 172, 184, 188, 262, 212, 272, 236, 248, 244, 304, 268, 346, 284, 328, 292, 386, 316, 398, 332, 376, 356, 458, 388, 478, 404, 472, 412, 526 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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 zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.
LINKS
EXAMPLE
The terms together with their prime indices begin:
1: {}
4: {1,1}
6: {1,2}
8: {1,1,1}
14: {1,4}
12: {1,1,2}
16: {1,1,1,1}
20: {1,1,3}
30: {1,2,3}
24: {1,1,1,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
52: {1,1,6}
48: {1,1,1,1,2}
MATHEMATICA
nn=20;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]], {i, Length[y]}];
seq=Table[wts[primeMS[n]], {n, 1, Prime[nn]^2}];
Table[Position[seq, k][[1, 1]], {k, 0, nn}]
CROSSREFS
First position of n in A359674, reverse A359677.
The sorted version is A359675, reverse A359680.
The reverse one-based version is A359679, sorted A359754.
The reverse version is A359681.
The one-based version is A359682, sorted A359755.
The version for standard compositions is A359756, one-based A089633.
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A124757 gives zero-based weighted sum of standard compositions, rev A231204.
A304818 gives weighted sums of prime indices, reverse A318283.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Sequence in context: A340960 A261680 A218465 * A050902 A320125 A110974
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Jan 14 2023
STATUS
approved

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Last modified March 2 09:28 EST 2024. Contains 370461 sequences. (Running on oeis4.)