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

1,1

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.

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A007617, A032447 (inverse of phi).

Sequence in context: A226129 A167368 A318165 * A068697 A010258 A363270

Adjacent sequences: A215237 A215238 A215239 * A215241 A215242 A215243

Keyword

nonn

Author

T. D. Noe, Oct 12 2012

Status

approved