A067170 -id:A067170 - cp's OEIS frontend

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

Joseph L. Pe, Feb 18 2002

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)

			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.

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

Cf. A006753, A067170.

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 *)

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

cp's OEIS Frontend

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.

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