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, 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
Offset: 1
Examples
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.
Links
- David A. Corneth, Table of n, a(n) for n = 1..11790 (first 260 terms from Giovanni Resta, terms < 10^34)
Programs
-
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[ # ] &] -
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
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
Comments