A215240 Sum of the numbers p such that phi(p) = n, where phi is Euler's totient function.

3, 13, 0, 35, 0, 48, 0, 105, 0, 33, 0, 166, 0, 0, 0, 231, 0, 138, 0, 218, 0, 69, 0, 621, 0, 0, 0, 87, 0, 93, 0, 581, 0, 0, 0, 655, 0, 0, 0, 833, 0, 276, 0, 299, 0, 141, 0, 1514, 0, 0, 0, 159, 0, 243, 0, 377, 0, 177, 0, 1114, 0, 0, 0, 1315, 0, 201, 0, 0, 0, 213, 0

Offset: 1

Author

T. D. Noe, Oct 12 2012

Keywords

• nonn

Comments

These terms (greater than 0) are not unique. The first duplicate appears at a(256) = a(2236) = 6711.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
• David M. Bressoud, A Course in Computational Number Theory (web page), CNT.m, Computational Number Theory Mathematica package.

Crossrefs

Cf. A002181 (smallest inverse), A006511 (largest inverse), A217842 (product of inverses).

Cf. A007617, A032447 (inverse of phi).

Programs

Mathematica

Needs["CNT`"]; Table[Total[PhiInverse[n]], {n, 100}]

PARI

a(n) = vecsum(invphi(n)); \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp

Formula

a(n) = 0 if and only if n is in A007617. - Amiram Eldar, Nov 15 2024