%I #6 Aug 04 2018 14:45:05
%S 2,8,15,35,55,88,108,162,195,225,256,363,370,386,419,427,437,508,782,
%T 998,1616,1633,1857,1901,3055,3091,4806,4816,5851,5905,6142,6179,6275,
%U 6297,6487,6674,7161,7221,7278,7293,7591,7715,13041,13100,13122,13130,13179
%N Indices i such that A305671(i) != A305671(i-1).
%t Block[{c = Select[Range[10^4], CompositeQ], s}, s = DivisorSigma[1, c]; 1 + Position[Partition[#, 2, 1], _?(UnsameQ @@ # &)][[All, 1]] &@ Array[If[Length@ # == 1, #[[1, 1]], 0] &@ Last@ SplitBy[SortBy[Tally@ Take[s, #], Last], Last] &, Length@ s]] (* _Michael De Vlieger_, Jul 22 2018 *)
%o (PARI) composite(n) = my(i=0); forcomposite(c=1, , i++; if(i==n, return(c)))
%o mcv(v) = my(w=vecsort(v, , 8), count=vector(#w), ind=0, i=0); for(x=1, #w, for(y=1, #v, if(w[x]==v[y], count[x]++))); for(k=1, #count, if(count[k]==vecmax(count), ind=k; i++)); if(i > 1, return(0), return(w[ind]))
%o a305671(n) = my(v=[]); for(k=1, n, v=concat(v, sigma(composite(k)))); mcv(v)
%o terms(n) = my(i=0); for(x=2, oo, if(a305671(x)!=a305671(x-1), print1(x, ", "); i++); if(i==n, break))
%o terms(11) \\ Print initial 11 terms of the sequence
%Y Cf. A305671, A305672, A305673, A305675, A305676.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Jun 08 2018
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