A245316 Concatenate n-th composite integer with concatenation of its prime factors in ascending order and the sum of its prime factors.

4224, 6235, 82226, 9336, 10257, 122237, 14279, 15358, 1622228, 182338, 202259, 213710, 2221113, 2422239, 255510, 2621315, 273339, 2822711, 3023510, 322222210, 3331114, 3421719, 355712, 36223310, 3821921, 3931316

Offset: 1

Author

Jahangeer Kholdi, Sep 15 2014

Keywords

• nonn
• base

Examples

			a(2)=6235 since 6=2*3, 2+3=5 and 6 is the second composite integer.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A245315.

Programs

Mathematica

f[n_]:=FactorInteger[n];con[A_]:=(v1={};l=Length[A];Do[v1=Join[v1,IntegerDigits[A[[k]]]],{k,l}];FromDigits[v1]);alfa[n_]:=(b=f[n];j=Length[b];c=Table[Table[b[[k]][[1]],{b[[k]][[2]]}],{k,j}];w={};Do[w=Join[w,c[[k]]],{k,j}];con[w]);omega[n_]:=(b=f[n];j=Length[b];c=Table[Table[b[[k]][[1]],{b[[k]][[2]]}],{k,j}];w={};Do[w=Join[w,c[[k]]],{k,j}];Total[w]);nao[n_]:=con[{n,alfa[n],omega[n]}];v=Select[Range[2,1000],!PrimeQ[#]&];Table[nao[v[[k]]],{k,26}]
compcat[n_]:=Module[{f=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[ n]]},FromDigits[ Join[IntegerDigits[n],Flatten[ IntegerDigits/@ f],IntegerDigits[ Total[f]]]]]; compcat/@Select[Range[40],CompositeQ] (* Harvey P. Dale, Dec 31 2021 *)