A051948 - OEIS

A051948

Numbers k such that k*sigma(k) == 2 (mod phi(k)).

2, 3, 4, 5, 6, 7, 11, 13, 17, 19, 22, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

R. K. Guy, Unsolved Problems Number Theory, B37.

LINKS

Table of n, a(n) for n=1..56.

Chris Nash, A solution to the Subbarao relation (There no other solutions besides 4, 6, 22 and the primes) (html, pdf)

Carlos Rivera, Puzzle 76, z(n)=sigma(n) + phi(n) - 2n, The Prime Puzzles & Problems Connection.

M. V. Subbarao, On two congruences for primality, Pacific Journal of Mathematics, 52 (1974), 261-268. (PDF)

MATHEMATICA

Select[Range[2, 250], Mod[#*DivisorSigma[1, #]-2, EulerPhi[#]]==0&] (* Harvey P. Dale, Sep 22 2021 *)

PROG

(PARI) a(n)=if(n<12, [2, 3, 4, 5, 6, 7, 11, 13, 17, 19, 22][n], prime(n-3)) \\ Charles R Greathouse IV, Aug 26 2011

CROSSREFS

Cf. A000010, A000203, A002270.

Sequence in context: A090563 A045745 A054010 * A193461 A192587 A174323

Adjacent sequences: A051945 A051946 A051947 * A051949 A051950 A051951

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Dec 21 1999

STATUS

approved