A070170 Numbers k such that sigma(k-phi(k)) = phi(k).

2, 15, 39, 255, 627, 939, 1431, 1581, 2409, 3459, 4797, 14289, 20619, 30987, 31935, 43791, 57291, 68991, 71193, 73749, 74841, 94671, 120669, 121227, 132297, 148161, 162843, 196449, 200787, 209451, 217191, 302907, 308937, 434733, 439959, 455961, 466701, 467109

Offset

1,1

Comments

All terms 2 < a(n) < 20000000 are odd and divisible by 3. Most are squarefree.

From numerical observation if n>31 : log(n)^10 < a(n) < log(n)^11.

Links

Donovan Johnson, Table of n, a(n) for n = 1..500

Maple

filter:= proc(n) local p; p:= numtheory:-phi(n); numtheory:-sigma(n - p) = p end proc:
select(filter, [$1..500000]); # Robert Israel, Oct 12 2025

Mathematica

Do[s=DivisorSigma[1, (n-EulerPhi[n])]-EulerPhi[n]; If[Equal[s, 0], Print[n]], {n, 1, 2000000}]
Select[Range[500000], With[{ep=EulerPhi[#]}, DivisorSigma[1, #-ep]==ep&]] (* Harvey P. Dale, Oct 11 2025 *)

Prog

(PARI) for(n=2, 2000000, if(sigma(n-eulerphi(n))==eulerphi(n), print1(n, ", ")))

Crossrefs

Cf. A000010, A000203, A051953, A070171.

Sequence in context: A214541 A180223 A070009 * A033568 A200156 A249997

Adjacent sequences: A070167 A070168 A070169 * A070171 A070172 A070173

Keyword

easy,nonn

Author

Benoit Cloitre and Labos Elemer, May 06 2002

Extensions

Edited by Charles R Greathouse IV, Oct 28 2009

Status

approved