A067184 Numbers n such that sum of the squares of the prime factors of n equals the sum of the squares of the digits of n.

2, 3, 5, 7, 250, 735, 792, 2500, 4992, 9075, 11760, 25000, 30625, 67914, 91476, 117600, 185625, 187278, 250000, 264992, 523908, 630784, 855360, 1082565, 1176000, 2395008, 2500000, 2546775, 2898350, 3608550, 3833280, 4299750, 4790016, 5899068, 8553600, 9243850

Offset

1,1

Comments

From David A. Corneth, Sep 28 2019: (Start)

If 10*m is in the sequence then so is 100*m.

The sum of squares of digits of a k-digit number is at most 81*k. Therefore any term with at most k digits is p-smooth where p is the largest prime < (81*k)^(1/2). (End)

Links

David A. Corneth, Table of n, a(n) for n = 1..14898 (terms < 10^20)

Example

The prime factors of 4992 are 2,3,13, the sum of whose squares = 182 = sum of the squares of 4,9,9,2; so 4992 is a term of the sequence.

Mathematica

f[n_] := Module[{a, l, t, r}, a = FactorInteger[n]; l = Length[a]; t = Table[a[[i]][[1]], {i, 1, l}]; r = Sum[(t[[i]])^2, {i, 1, l}]]; g[n_] := Module[{b, m, s}, b = IntegerDigits[n]; m = Length[b]; s = Sum[(b[[i]])^2, {i, 1, m}]]; Select[Range[2, 10^5], f[ # ] == g[ # ] &]
Select[Range[2, 4300000], Total[Transpose[FactorInteger[#]][[1]]^2]== Total[ IntegerDigits[#]^2]&] (* Harvey P. Dale, Sep 01 2011 *)

Crossrefs

Cf. A006753, A067170.

Sequence in context: A064157 A257483 A178371 * A067170 A090719 A088297

Adjacent sequences: A067181 A067182 A067183 * A067185 A067186 A067187

Keyword

base,nonn

Author

Joseph L. Pe, Feb 18 2002

Extensions

a(16)-a(32) from Donovan Johnson, Sep 29 2009

Status

approved