OFFSET
1,1
COMMENTS
Conjecture: a(n) < 2*n for any n > 2.
Numbers n such that a(n) > n: 1, 2, 3, 8, 11, 14, 48, 227, 908, 4478, ... The next number, if it exists, is greater than 10^5. - Derek Orr, Sep 29 2014
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = 12 since 12 + 2 = 14 divides sigma(12)*phi(2) = 28.
MATHEMATICA
Do[m=1; Label[aa]; If[Mod[DivisorSigma[1, m]*EulerPhi[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m= m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 70}]
lpim[n_]:=Module[{m=1, ephn=EulerPhi[n]}, While[Mod[ephn*DivisorSigma[1, m], m+n]!=0, m++]; m]; Array[lpim, 70] (* Harvey P. Dale, Feb 14 2024 *)
PROG
(PARI)
a(n)=m=1; while((eulerphi(n)*sigma(m))%(m+n), m++); m
vector(100, n, a(n)) \\ Derek Orr, Sep 29 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 29 2014
STATUS
approved