A177053 Numbers k such that sum of the decimal digits of k is a quadratic residue modulo k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 17, 18, 22, 27, 31, 36, 37, 38, 39, 40, 41, 45, 54, 58, 62, 63, 66, 71, 72, 74, 77, 79, 81, 82, 83, 86, 88, 89, 90, 97, 100, 103, 106, 108, 111, 112, 114, 117, 121, 122, 126, 130, 131, 133, 135, 137, 138, 139, 141, 144, 150, 153, 156, 157, 159, 161, 162, 163, 167, 169, 171, 177, 178, 179, 180

Offset

1,2

Links

Table of n, a(n) for n=1..77.

Example

159 is in the sequence because L((1+5+9)/159) = L(15/159) = 1 where L(a/b) is the Legendre symbol of a and b, which is defined to be 1 if a is a quadratic residue (mod b) and -1 if a is a quadratic non-residue (mod b).

Maple

isA177053 := proc(n) is(numtheory[quadres](A007953(n), n) =1 ); end proc:
for n from 1 to 140 do if isA177053(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Dec 12 2010

Prog

(PARI) isok(n) = issquare(Mod(sumdigits(n), n)); \\ Michel Marcus, Feb 01 2016

Crossrefs

Sequence in context: A247810 A247800 A092968 * A151547 A008817 A076356

Adjacent sequences: A177050 A177051 A177052 * A177054 A177055 A177056

Keyword

nonn,base

Author

Michel Lagneau, Dec 09 2010

Status

approved