This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a[n_]:=Total[Select[Range[n],PrimeOmega[#]==2&]];Array[a,58,0] (* James C. McMahon, Jul 06 2025 *)
a(5) = 18 = 1 + 2 + 3 + 5 + 7.
Accumulate[Select[Range[100],PrimeOmega[#]!=2&]] (* Harvey P. Dale, Aug 22 2021 *)
For n = 6 the set of all divisors of 6 greater than 1 is {2, 3, 6}. Also, the set of all a(n < 6) is {0, 1, 2, 3}. The greatest divisor of 6 (excluding 1) that has been listed is 3, so a(6) = 3.
a = 0; A = {a}; Do[s = Drop[Reverse[Divisors[n]], 1]; s = Drop[s, -1]; If[Length[s] >= 1, Do[If[MemberQ[A, Part[s, d]], AppendTo[A, Part[s, d]]; Break[]], {d, 1, Length[s]}], a++; AppendTo[A, a]], {n, 2, 77}] Print[A]
first(n)=my(v=vector(n),m); forfactored(k=2,n, v[k[1]]=if(vecsum(k[2][,2])==1, m++, my(t); fordiv(k,d, if(d<=m, t=d)); t)); v \\ Charles R Greathouse IV, Oct 14 2022
13 is a term, because (1 + 4 + 6 + 8 + 9 + 10 + 12) - (2 + 3 + 5 + 7 + 11 + 13) = 3^2.
a373945(upto=10^8) = {my(s=-1, pp=2); print1(0,", ",1,", "); forprime (p=3, upto, for (k=pp+1, p-1, s+=k; if (issquare(s), print1(k,", "))); s-=p; if (issquare(s), print1(p,", ")); pp=p)};
a373945() \\ Hugo Pfoertner, Jun 23 2024
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