|
Search: id:A067688
|
|
|
| A067688 |
|
Composite n such that for some integer r, n equals the sum of the r-th powers of the prime factors of n (counted with multiplicity). |
|
+0
3
|
|
| 4, 16, 27, 256, 3125, 19683, 65536, 823543, 1096744, 2836295, 4294967296, 4473671462
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Every prime is the sum of the first powers of its prime factors, so only composite numbers have been considered in this sequence.
Every integer of the form p^p^k with p prime and k>0 is in the sequence, since it equals the sum of the (p^k - k)-th powers of its prime factors. The first 8 terms of the sequence are of this form, but 1096744 = 2^3*11^3*103 and 2836295 = 5*7*11*53*139 are not.
4473671462=2*13*179*593*1621 is also not a prime power.
|
|
EXAMPLE
|
The sum of the cubes of the prime factors of 1096744 is 3*2^3 + 3*11^3 + 103^3 = 1096744.
|
|
MATHEMATICA
|
For[n=2, True, n++, If[ !PrimeQ[n], For[r=1; fn=FactorInteger[n]; s=0, s<=n, r++, s=Plus@@((#[[2]]#[[1]]^r)&/@fn); If[s==n, Print[{n, r}]]]]]
|
|
CROSSREFS
|
Cf. A068916, A081177 (for values of r).
Adjacent sequences: A067685 A067686 A067687 this_sequence A067689 A067690 A067691
Sequence in context: A008478 A137231 A111260 this_sequence A046358 A046366 A097374
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 04 2002
|
|
EXTENSIONS
|
Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 07 2002
More terms from Jud McCranie (j.mccranie(AT)comcast.net), Mar 10 2003
|
|
|
Search completed in 0.002 seconds
|
