A095409 -id:A095409 - cp's OEIS frontend

A095411 Numbers k such that total number of decimal digits of all distinct prime factors of k is larger than the number of digits of k.

6, 22, 26, 30, 33, 34, 38, 39, 42, 44, 46, 51, 52, 55, 57, 58, 60, 62, 65, 66, 68, 69, 70, 74, 76, 77, 78, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 99, 102, 110, 114, 130, 132, 138, 143, 154, 156, 165, 170, 174, 182, 186, 187, 190, 195, 198, 202, 204, 206, 209

Offset: 1

Labos Elemer, Jun 21 2004

			For k=55: 2 digits, prime set={5,11} with {5,1,1} digits, 3>2, so 55 is a term.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A055642, A095407, A095408, A095409, A095410.

q[n_] := Total[IntegerLength /@ FactorInteger[n][[;; , 1]]] > IntegerLength[n]; q[1] = False; Select[Range[210], q] (* Amiram Eldar, Mar 25 2025 *)

Solutions to A095407(x) > A055642(x).

Name corrected by Amiram Eldar, Mar 25 2025

A095410 Numbers n such that total number of decimal digits of all distinct prime factors of n equals the number of digits of n.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 28, 29, 31, 35, 36, 37, 40, 41, 43, 45, 47, 48, 50, 53, 54, 56, 59, 61, 63, 67, 71, 72, 73, 75, 79, 80, 83, 89, 96, 97, 98, 101, 103, 104, 105, 106, 107, 109, 111, 113, 115, 116, 117, 118, 119, 120, 122

Offset: 1

Labos Elemer, Jun 21 2004

			n=184, 3 digits,prime set={2,23} also with 3 digits {2,2,3}.

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

Cf. A055642, A095407, A095408, A095409, A095411.

ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] pl[x_] :=Length[tdp[x]] nl[x_] :=Length[IntegerDigits[x]] t1=Table[nl[w], {w, 1, 1000}];t2=Table[pl[w], {w, 1, 1000}];t2-t1 Flatten[Position[t2-t1, 0]]
Rest[Select[Range[200],Length[Flatten[IntegerDigits/@Transpose[ FactorInteger[ #]][[1]]]]==IntegerLength[#]&]] (* Harvey P. Dale, Oct 22 2011 *)

Solutions to A095407[x]=A055642[x].

cp's OEIS Frontend

A095411 Numbers k such that total number of decimal digits of all distinct prime factors of k is larger than the number of digits of k.

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