A095404 -id:A095404 - cp's OEIS frontend

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

Labos Elemer, Jun 21 2004

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

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

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

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 *)

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

A095406 Numbers n such that Sum-of-digits-of-n < Sum-of-digits-of-all-distinct-prime-factors-of-n.

Original entry on oeis.org

10, 12, 14, 15, 20, 21, 30, 34, 35, 38, 40, 42, 50, 51, 57, 60, 63, 70, 74, 90, 91, 95, 100, 102, 104, 105, 106, 110, 111, 112, 114, 115, 116, 118, 119, 120, 122, 123, 126, 130, 132, 133, 134, 140, 141, 142, 145, 146, 150, 152, 153, 154, 158, 161, 170, 171, 174

Offset: 1

Labos Elemer, Jun 21 2004

			n=38: digit sum=11, prime factor-digit sum=2+1+9=12>11, so 38 is here;
n=10^j:digit sum=1, prime factor-digit sum=2+5=7?1. so 10^j is here for all j [this implies that the sequence is infinite].

Cf. A007953, A051351, A095402, A095403, A095404, A095405.

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]]
Select[Range[200],Total[IntegerDigits[#]]Harvey P. Dale, May 06 2012 *)

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

cp's OEIS Frontend

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

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