A071390 -id:A071390 - cp's OEIS frontend

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

Labos Elemer, May 23 2002

			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.

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

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

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

a(n) = for(m=1, n, if(sigma(m)+eulerphi(m)==n, return(m))); 0; \\ Jinyuan Wang, Jul 29 2020

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

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

A072808 Smallest m such that sigma(m) mod phi(m) = n or 0 if no solution exists.

Original entry on oeis.org

4, 5, 8, 24, 0, 22, 16, 21, 450, 40, 25, 48, 50, 136, 32, 110, 100, 90, 144, 88, 0, 656, 121, 102, 0, 80, 169, 96, 0, 68, 64, 55, 676, 464, 289, 65, 0, 117, 162, 91, 0, 116, 225, 85, 0, 272, 529, 95, 0, 148, 288, 133, 0, 164, 0, 115, 0, 160, 841, 147, 0, 333, 128, 247

Offset: 1

Labos Elemer, Jul 12 2002

nonn

Warning: It is only conjectured that there are no solutions for n such that a(n) = 0. The search for solutions tested all m <= 10^10 for these n.
For odd remainders a(n) is a square or twice a square. See A028982, except terms 1 and 2.
All zeros corresponding to odd terms a(n) with n < 64 confirmed up to m <= 10^24. - Giovanni Resta, Apr 02 2020

			For n=4: a(4)=24 since sigma(24)=60, phi(24)=8 and Mod(60, 8)=4.

Cf. A000203, A000010, A028982, A063514, A067192, A067193, A071390.

V:= Vector(100):
for m from 2 to 10^7 do
 v:= numtheory:-sigma(m) mod numtheory:-phi(m);
 if v > 0 and v <= 100 and V[v] = 0 then V[v]:= m fi
od:
convert(V,list); # Robert Israel, Nov 30 2024

f[x_] := Mod[DivisorSigma[1, x], EulerPhi[x]]; t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000000}]; t

a(n) = Min{x; Mod(A000203(x), A000010(x))=n} or 0 if no solutions.

Name corrected by Sean A. Irvine, Oct 30 2024

Name corrected by Robert Israel, Nov 30 2024

cp's OEIS Frontend

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

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