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.

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

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