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A132630 Numbers n such that sigma(n)-n divides sigma(n+1)-n-1, where sigma(n) is sum of positive divisors of n. 2
2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With the exception of the first term, only odd numbers. All the prime numbers p are included because sigma(p)-p=1.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

n=85 -> sigma(n+1)-n-1=1+2+43=46 sigma(n)-n=1+5+17=23 -> 46/23=2

n=125 -> sigma(n+1)-n-1=1+2+3+6+7+9+14+18+21+42+63=186 sigma(n)-n=1+5+25=31 -> 186/31=6

MAPLE

with(numtheory); P:=proc(n) local a, i; for i from 1 by 1 to n do if sigma(i)-i>0 then a:=(sigma(i+1)-i-1)/(sigma(i)-i); if a>0 and trunc(a)=a then print(i); fi; fi; od; end: P(200)

MATHEMATICA

Select[Range[2, 200], Divisible[DivisorSigma[1, #+1]-#-1, DivisorSigma[ 1, #]-#]&] (* Harvey P. Dale, Apr 25 2015 *)

PROG

(MAGMA) [k:k in [2..200]| IsIntegral((DivisorSigma(1, k+1)-k-1)/ (DivisorSigma(1, k)-k))]; // Marius A. Burtea, Nov 06 2019

CROSSREFS

Cf. A132585, A132586, A132631.

Sequence in context: A301987 A316857 A318589 * A033946 A328232 A189710

Adjacent sequences:  A132627 A132628 A132629 * A132631 A132632 A132633

KEYWORD

easy,nonn

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Aug 27 2007

EXTENSIONS

Comment amended by Harvey P. Dale, Apr 25 2015

STATUS

approved

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Last modified April 5 21:31 EDT 2020. Contains 333260 sequences. (Running on oeis4.)