A071391 Least number m such that sigma(m) + phi(m) = n or 0 if no such number exists.

0, 1, 0, 2, 0, 3, 0, 0, 4, 5, 0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 10, 0, 0, 0, 13, 0, 0, 0, 14, 0, 12, 0, 17, 0, 0, 0, 19, 16, 0, 0, 0, 0, 21, 18, 22, 0, 0, 0, 20, 25, 0, 0, 26, 0, 0, 0, 27, 0, 0, 0, 31, 0, 0, 0, 0, 0, 24, 0, 34, 0, 35, 0, 37, 0, 0, 0, 38, 32, 30, 0, 41, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0

Offset

1,4

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a(n) = Min{x; A000203(x)+A000010(x)=n} or a(n) = 0 if no solution exists.

Example

n=256: a(256) = 110, sigma(110) + phi(110) = 216 + 40 = 256 = n and no positive integer k < 110 has sigma(k) + phi(k) = 256.

Mathematica

f[x_] := DivisorSigma[1, x]+EulerPhi[x] t=Table[0, {100}]; Do[c=f[n]; If[c<101&&t[[c]]==0, t[[c]]=n], {n, 1, 1000000}]; t

Prog

(PARI) a(n) = for(m=1, n, if(sigma(m)+eulerphi(m)==n, return(m))); 0; \\ Jinyuan Wang, Jul 29 2020
(PARI) first(n) = { my(v = vector(n)); for(i = 1, n, c = sigma(i) + eulerphi(i); if(c <= n, if(v[c] == 0, v[c] = i ) ) ); v } \\ David A. Corneth, Jul 30 2020

Crossrefs

Cf. A000010, A000203, A065387, A051612, A071390.

Sequence in context: A131104 A141701 A167990 * A102390 A127640 A113303

Adjacent sequences: A071388 A071389 A071390 * A071392 A071393 A071394

Keyword

nonn,easy

Author

Labos Elemer, May 23 2002

Status

approved