|
| |
|
|
A161917
|
|
Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors.
|
|
2
| |
|
|
12, 15, 35, 42, 60, 63, 66, 68, 84, 90, 95, 110, 114, 119, 140, 143, 152, 168, 189, 195, 204, 209, 216, 234, 245, 258, 264, 270, 280, 287, 290, 294, 297, 319, 322, 323, 352, 368, 377, 380, 384, 396, 470, 476, 480, 506, 510, 527, 531, 544, 552, 558, 559, 572
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
FORMULA
| {n: A001414(n) | A000203(n)}. [R. J. Mathar, Jun 26 2009]
|
|
|
EXAMPLE
| n=12: Sum_divisors (1,2,3,4,6,12) = 28; Sum_prime_factors (2,2,3) =7 -> 28/7 = 4. n=319: Sum_divisors (1,11,29,319) = 360; Sum_prime_factors (11,29) =40 -> 360/40 = 9.
|
|
|
MAPLE
| with(numtheory); P:=proc(i) local b, c, j, s, n; for n from 2 by 1 to i do b:=(convert(ifactors(n), `+`)-1); c:=nops(b); j:=0; s:=0; for j from c by -1 to 1 do s:=s+convert(b[j], `*`); od; if trunc(sigma(n)/s)=sigma(n)/ s then print(n, s, sigma(n), sigma(n)/s); fi; od; end: P(1000);
|
|
|
MATHEMATICA
| Select[Range[2, 600], Divisible[DivisorSigma[1, #], Total[Times@@@FactorInteger[#]]]&]
|
|
|
CROSSREFS
| Cf. A161918
Sequence in context: A134221 A179148 A194234 * A065150 A087098 A109315
Adjacent sequences: A161914 A161915 A161916 * A161918 A161919 A161920
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Jun 23 2009
|
|
|
EXTENSIONS
| Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2009
Mathematica program provided by Harvey P. Dale, Dec 09, 2010
|
| |
|
|
