A256527 a(n) is the least number k > 0 such that sigma(k) = phi(n*k).

1, 1, 15, 3, 14, 6, 6, 42, 30, 42, 168, 210, 210, 420, 840, 20790, 20790, 9240, 9240, 83160, 120120, 3984120, 5165160, 43825320, 26860680, 43825320, 1304863560, 569729160, 569729160, 16522145640, 18176198040, 563462139240, 1140028049160, 3844800479520, 1255683068640

Offset

1,3

Links

Table of n, a(n) for n=1..35.

Formula

For n >= 5, a(n) = A087979(n). - Conjectured by Manfred Scheucher, May 28 2015; proved by Max Alekseyev, Sep 29 2023

Example

sigma(1)  = phi(1*1)  = 1;
sigma(1)  = phi(2*1)  = 1;
sigma(15) = phi(3*15) = 24;
sigma(3)  = phi(4*3)  = 4;
sigma(14) = phi(5*14) = 24;
sigma(6)  = phi(6*6)  = 12;
sigma(6)  = phi(7*6)  = 12;
sigma(42) = phi(8*42) = 96;
sigma(30) = phi(9*30) = 72; etc.

Maple

with(numtheory): P:=proc(q) local k, n;
for n from 1 to q do for k from 1 to q do
if sigma(k)=phi(k*n) then lprint(n, k); break; fi;
od; od; end: P(10^5);

Mathematica

Table[k = 1; While[DivisorSigma[1, k] != EulerPhi[n k], k++]; k, {n, 20}] (* Michael De Vlieger, May 28 2015 *)

Prog

(PARI) a(n) = {k=1; while(sigma(k) != eulerphi(n*k), k++); k; } \\ Michel Marcus, Apr 01 2015

Crossrefs

Except for a(4), same as A087979.

Cf. A000010, A000203, A241762.

Sequence in context: A174680 A225948 A248129 * A040219 A317315 A330361

Adjacent sequences: A256524 A256525 A256526 * A256528 A256529 A256530

Keyword

nonn

Author

Paolo P. Lava, Apr 01 2015

Extensions

a(21)-a(23) from Michel Marcus, Apr 01 2015

a(24)-a(26) from Jon E. Schoenfield, Jun 28 2015

a(27)-a(35) from Giovanni Resta, May 24 2016

Status

approved