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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. 3
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 * A242270 A152126 A065858

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 March 29 15:05 EDT 2017. Contains 284273 sequences.