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 A161918 Numbers n such that the sum of the divisors minus the sum of the prime factors (counted with multiplicity) is equal to n+1. 4
 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; text; internal format)
 OFFSET 1,1 COMMENTS Equals A006881 union {8}. - Franklin T. Adams-Watters, Jun 26 2009 LINKS Jayanta Basu, Table of n, a(n) for n = 1..10000 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. 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); MATHEMATICA Select[Range[203], DivisorSigma[1, #] - Total[Times @@@ FactorInteger[#]] == # + 1 &] (* Jayanta Basu, Aug 11 2013 *) 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", ")) CROSSREFS Cf. A161917, A006881, A151797, A030229. Sequence in context: A211337 A007422 A030513 * A294729 A242270 A298252 Adjacent sequences: A161915 A161916 A161917 * A161919 A161920 A161921 KEYWORD easy,nonn AUTHOR Paolo P. Lava and Giorgio Balzarotti, Jun 23 2009 EXTENSIONS Edited by N. J. A. Sloane, Jun 27 2009 incorporating suggestions from R. J. Mathar, M. F. Hasler, Benoit Jubin and others. STATUS approved

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Last modified September 15 09:55 EDT 2024. Contains 375932 sequences. (Running on oeis4.)