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A161918
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Numbers n such that the sum of the divisors minus the sum of the prime factors (counted with multiplicity) is equal to n+1.
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2
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6, 8, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Equals A006881 union {8}. - Franklin T. Adams-Watters, Jun 26 2009
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EXAMPLE
| n=21: Sum_divisors (1,3,7,21) = 32; Sum_prime_factors (3,7) = 10 -> 32-10 = 22. n=55: Sum_divisors (1,5,11,55) = 72; Sum_prime_factors (5,11) = 16 -> 72-16 = 56.
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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 n=sigma(n)-s-1 then print(n); fi; od; end: P(500);
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PROG
| (PARI from M. F. Hasler):
isA161918(n)={ n+1 == sigma(n)-(n=factor(n))[, 1]~*n[, 2] }
for(n=1, 500, isA161918(n)&print1(n", "))
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CROSSREFS
| Cf. A161917, A006881, A151797, A030229.
Sequence in context: A036455 A007422 A030513 * A152126 A065858 A073582
Adjacent sequences: A161915 A161916 A161917 * A161919 A161920 A161921
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KEYWORD
| easy,nonn
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Jun 23 2009
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EXTENSIONS
| Edited by N. J. A. Sloane, Jun 27 2009 incorporating suggestions from R. J. Mathar, M. F. Hasler, Benoit Jubin and others.
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