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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
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 (list; graph; refs; listen; history; text; internal format)
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..15800 (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

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Last modified January 27 15:14 EST 2020. Contains 331295 sequences. (Running on oeis4.)