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A067170 Numbers n such that sum of the cubes of the distinct prime factors of n equals the sum of the cubes of the digits of n. 2
2, 3, 5, 7, 250, 735, 2500, 25000, 250000, 1858560, 2500000, 18585600, 25000000, 91990080, 185856000, 242121642, 250000000, 919900800, 1081088775, 1390120992, 1768635648, 1858560000, 2500000000, 5435938431, 7245987840, 9199008000, 9475854336, 17996666688, 18585600000, 24214634829, 25000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If 10*m is a term (e.g. m = 25, 185856, 9199008), then 10^k * m is a term for all k >= 1. Therefore this sequence is infinite. - Amiram Eldar, Sep 28 2019

The sum of cubes of digits of a k-digit number is at most 729*k. Therefore any term with at most k digits is p-smooth where p is the largest prime < (729*k)^(1/3). - David A. Corneth, Sep 28 2019

LINKS

David A. Corneth, Table of n, a(n) for n = 1..11790 (first 260 terms from Giovanni Resta, terms < 10^34)

EXAMPLE

The prime factors of 735 are 3,5,7, the sum of whose cubes = 495 = sum of the cubes of the digits of 735; so 735 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]])^3, {i, 1, l}]]; g[n_] := Module[{b, m, s}, b = IntegerDigits[n]; m = Length[b]; s = Sum[(b[[i]])^3, {i, 1, m}]]; Select[Range[2, 10^6], f[ # ] == g[ # ] &]

PROG

(PARI) sd(n) = my(d=digits(n)); sum(k=1, #d, d[k]^3); \\ A055012

sp(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]^3); \\ A005064

isok(n) = sp(n) == sd(n); \\ Michel Marcus, Sep 28 2019

CROSSREFS

Cf. A005064, A006753, A055012, A067184.

Sequence in context: A257483 A178371 A067184 * A090719 A088297 A180015

Adjacent sequences:  A067167 A067168 A067169 * A067171 A067172 A067173

KEYWORD

nonn,base

AUTHOR

Joseph L. Pe, Feb 18 2002

EXTENSIONS

a(10)-a(14) from Amiram Eldar, Sep 28 2019

a(15)-a(18) from Michel Marcus, Sep 28 2019

a(20)-a(29) from David A. Corneth, Sep 28 2019

Missing a(19) from Giovanni Resta, Sep 28 2019

STATUS

approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)