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Search: id:A161917
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| A161917 |
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Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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FORMULA
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{n: A001414(n) | A000203(n)}. [R. J. Mathar, Jun 26 2009]
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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A161918
Sequence in context: A015904 A124521 A134221 this_sequence A065150 A087098 A109315
Adjacent sequences: A161914 A161915 A161916 this_sequence A161918 A161919 A161920
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jun 23 2009
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EXTENSIONS
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Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2009
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