

A359676


Least positive integer whose weakly increasing prime indices have zerobased 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
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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 zerobased weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i1)*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[(i1)*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

A053632 counts compositions by zerobased weighted sum.
A124757 gives zerobased weighted sum of standard compositions, rev A231204.


KEYWORD



AUTHOR



STATUS

approved



