A143869 An integer k is called regular (mod n) if there is an integer x such that k^2 x == k (mod n). Then these numbers are the sum of regular integers k (mod n) such that 1 <= k <= n for n=1,2,... .

1, 3, 6, 8, 15, 21, 28, 24, 36, 55, 66, 60, 91, 105, 120, 80, 153, 135, 190, 160, 231, 253, 276, 192, 275, 351, 270, 308, 435, 465, 496, 288, 561, 595, 630, 396, 703, 741, 780, 520, 861, 903, 946, 748, 810, 1081, 1128, 672, 1078, 1075, 1326, 1040, 1431, 1053

Offset: 1

Author

Laszlo Toth, Sep 04 2008

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Osama Alkam and Emad Abu Osba, On the regular elements in Zn, Turk J Math, 32 (2008), 31-39.
• B. Apostol and L. Petrescu, Extremal Orders of Certain Functions Associated with Regular Integers (mod n), Journal of Integer Sequences, 2013, # 13.7.5.
• L. Tóth, Regular integers modulo n, Annales Univ. Sci. Budapest., Sect. Comp., 29 (2008), 263-275.

Crossrefs

Cf. A055653, A176345.

Programs

PARI

isregu(k, n) = {g = gcd(k, n); if ((n % g == 0) && (gcd(g, n/g) == 1), return(k), return(0));}
a(n) = sum(k=1, n, isregu(k, n)) \\ Michel Marcus, May 25 2013

Formula

a(n) = n*(A055653(n)+1)/2.

Extensions

Extended by R. J. Mathar, Sep 05 2008