OFFSET
1,2
COMMENTS
EXAMPLE
The divisors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60}, and the distinct subset-sums of its prime indices {1,1,2,3} are {0,1,2,3,4,5,6,7}, so the difference is 12 - 8 = 4. Since 60 is the first number with this difference, we have a(4) = 60.
The terms together with their prime indices begin:
1: {}
12: {1,1,2}
24: {1,1,1,2}
48: {1,1,1,1,2}
60: {1,1,2,3}
120: {1,1,1,2,3}
144: {1,1,1,1,2,2}
180: {1,1,2,2,3}
192: {1,1,1,1,1,1,2}
240: {1,1,1,1,2,3}
336: {1,1,1,1,2,4}
360: {1,1,1,2,2,3}
420: {1,1,2,3,4}
630: {1,2,2,3,4}
720: {1,1,1,1,2,2,3}
840: {1,1,1,2,3,4}
900: {1,1,2,2,3,3}
960: {1,1,1,1,1,1,2,3}
MATHEMATICA
nn=1000;
w=Table[DivisorSigma[0, n]-Length[Union[Total/@Subsets[prix[n]]]], {n, nn}];
spnm[y_]:=Max@@Select[Union[y], Function[i, Union[Select[y, #<=i&]]==Range[0, i]]];
Table[Position[w, k][[1, 1]], {k, 0, spnm[w]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 09 2023
STATUS
approved