A069825 -id:A069825 - cp's OEIS frontend

A291503 a(n) is the smallest k such that sigma(k) = phi(n), or 0 if no such k exists.

1, 1, 0, 0, 3, 0, 5, 3, 5, 3, 0, 3, 6, 5, 7, 7, 0, 5, 10, 7, 6, 0, 0, 7, 19, 6, 10, 6, 12, 7, 29, 0, 19, 0, 14, 6, 22, 10, 14, 0, 27, 6, 20, 19, 14, 0, 0, 0, 20, 19, 21, 14, 0, 10, 27, 14, 22, 12, 0, 0, 24, 29, 22, 21, 33, 19, 0, 21, 43, 14, 0, 14, 30, 22, 27, 22, 24, 14, 45

Offset: 1

Altug Alkan, Aug 25 2017

			a(5) = 3 because sigma(3) = phi(5) and 3 is the smallest number with this property.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000010, A000203, A051444, A069825.

N:= 100: # to get a(1)..a(N)
R:= Vector(N):
for k from 1 to N-1 do
  s:= numtheory:-sigma(k);
  if s <= N and R[s] = 0 then R[s]:= k fi;
od:
seq(R[numtheory:-phi(n)],n=1..N); # Robert Israel, Aug 25 2017

a(n) = for(k=1, eulerphi(n), if(sigma(k)==eulerphi(n), return(k))); 0 \\ after Charles R Greathouse IV at A051444

a(A069825(n)) = 0 for n > 1.

a(n) = A051444(A000010(n)). - Michel Marcus, Aug 25 2017

A291524 Numbers m such that psi(x) = phi(m) has a solution while sigma(y) = phi(m) has none.

Original entry on oeis.org

751, 919, 1502, 1838, 2841, 3788, 5682, 6629, 8523, 11251, 11937, 13258, 13669, 14205, 15137, 15152, 15397, 15607, 15916, 16099, 17046, 18940, 19895, 22502, 22728, 23874, 27338, 28410, 30103, 30274, 30304, 30794, 31214, 31832, 32198, 36853, 37880, 39790, 43657

Offset: 1

Altug Alkan, Aug 25 2017

nonn

Values of A069825(k) such that psi(x) = phi(A069825(k)) has a solution for k > 1.

Prime terms are 751, 919, 11251, 13669, 15137, ...

			751 is a term because psi(x) = phi(751) = 750 has a solution that is x = 625 while there is no solution for sigma(y) = phi(751) = 750.

Cf. A000010, A000203, A001615, A069825.

is1(n) = my(N=eulerphi(n)); for(k=1, N, if(sigma(k)==N, return(1))); 0;
a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));
is2(n) = my(N=eulerphi(n)); for(k=1, N, if(a001615(k)==N, return(1))); 0;
isok(n) = !is1(n) && is2(n); \\ after Charles R Greathouse IV at A001615

cp's OEIS Frontend

A291503 a(n) is the smallest k such that sigma(k) = phi(n), or 0 if no such k exists.

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