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A177053 Numbers k such that sum of the decimal digits of k is a quadratic residue modulo k. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 21:53 EDT 2020. Contains 337173 sequences. (Running on oeis4.)