A095405 Numbers n such that Sum-of-digits-of-n = Sum-of-digits-of-all-distinct-prime-factors-of-n.

2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 29, 31, 37, 41, 43, 47, 53, 58, 59, 61, 67, 71, 73, 79, 83, 84, 85, 89, 94, 97, 101, 103, 107, 109, 113, 127, 131, 136, 137, 139, 149, 151, 157, 160, 163, 166, 167, 173, 179, 181, 191, 193, 197, 199, 202, 211, 223, 227, 229, 233, 234

Offset: 1

Author

Labos Elemer, Jun 21 2004

Keywords

• nonn
• base

Examples

			n=85: digit sum=13, prime factor-digit sum=5+1+7=13, so 85 is here.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007953, A051351, A095402, A095403, A095404, A095406.

Programs

Mathematica

ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] a=Table[sd[w], {w, 1, 256}];b=Table[sdp[w], {w, 1, 150}];b-a; Flatten[Position[Sign[b-a], 0]]
Select[Range[2,300],Total[Flatten[IntegerDigits/@FactorInteger[#][[All, 1]]]] == Total[IntegerDigits[#]]&] (* Harvey P. Dale, Sep 29 2019 *)

Formula

Solutions to A007953[x]=A095402[x].