A327172 If there is a divisor d of n such that phi(d)*d = n, then a(n) = d, otherwise a(n) = 0.

1, 2, 0, 0, 0, 3, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 10, 0, 7, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15

Offset: 1

Author

Antti Karttunen, Sep 28 2019

Keywords

• nonn

Comments

If such a divisor exists, it is necessarily unique. See Franz Vrabec's Dec 12 2012 comment in A002618.

Each natural number n > 0 occurs exactly once in this sequence, at position A002618(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..21000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Left inverse of A002618.

Cf. A000010.

Cf. A082473 (the indices of nonzero terms), A194507 (nonzero terms in the order of appearance).

Programs

Mathematica

With[{s = EulerPhi /@ Range@ 120}, Table[DivisorSum[n, # &, # s[[#]] == n &], {n, Length@ s}]] (* Michael De Vlieger, Sep 29 2019 *)

PARI

A327172(n) = { fordiv(n,d,if(eulerphi(d)*d == n, return(d))); (0); };

Formula

a(A002618(n)) = n.

a(A082473(n)) = A194507(n).