A095404 Numbers n such that Sum-of-digits-of-n > Sum-of-digits-of-all-distinct-prime-factors-of-n.

1, 4, 6, 8, 9, 16, 18, 24, 25, 26, 27, 28, 32, 33, 36, 39, 44, 45, 46, 48, 49, 52, 54, 55, 56, 62, 64, 65, 66, 68, 69, 72, 75, 76, 77, 78, 80, 81, 82, 86, 87, 88, 92, 93, 96, 98, 99, 108, 117, 121, 124, 125, 128, 129, 135, 138, 143, 144, 147, 148, 155, 156, 159, 162, 164

Offset

1,2

Links

Table of n, a(n) for n=1..65.

Formula

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

Example

n=24: digit sum=6, prime factor-digit sum=2+3=5, so 24 is here;
n=153: digit sum=9, prime factor-digit sum=3+5+3=11>9, so 153 is here.

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], 1]]

Crossrefs

Cf. A007953, A051351, A095402, A095403, A095405, A095406.

Sequence in context: A228019 A228020 A163282 * A073540 A123710 A075243

Adjacent sequences: A095401 A095402 A095403 * A095405 A095406 A095407

Keyword

nonn,base

Author

Labos Elemer, Jun 21 2004

Status

approved