A248030 Least positive integer m such that m + n divides sigma(m)*phi(n), where sigma(.) and phi(.) are given by A000203 and A000010.

2, 12, 4, 2, 3, 6, 2, 10, 3, 2, 21, 8, 3, 22, 13, 8, 9, 6, 8, 12, 3, 8, 10, 4, 5, 10, 21, 8, 20, 26, 4, 8, 7, 14, 13, 12, 8, 4, 33, 8, 23, 6, 20, 12, 3, 16, 22, 72, 7, 10, 13, 4, 27, 42, 5, 24, 15, 26, 57, 18, 11, 38, 27, 20, 31, 4, 21, 36, 19, 2

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

Cf. A000010, A000203, A248004, A248007, A248008, A248029.

Sequence in context: A317206 A164869 A347408 * A082292 A248588 A332350

Adjacent sequences: A248027 A248028 A248029 * A248031 A248032 A248033

Keyword

nonn

Author

Zhi-Wei Sun, Sep 29 2014

Status

approved