

A067207


Numbers k such that the digits of sigma_2(k) end in k.


0




OFFSET

1,2


COMMENTS

Recall that sigma_2(k) denotes the sum of the squares of the divisors of k.
No more terms between 7060 and 420000.  R. J. Mathar, May 30 2010
No additional terms up to 10 million.  Harvey P. Dale, Dec 09 2014


LINKS

Table of n, a(n) for n=1..5.


EXAMPLE

The divisors of 81 are 1,3,9,27,81, the sum of whose squares = 7381 which ends in 81, so 81 is a term of the sequence.


MAPLE

endswith := proc(a, b) local dgsa, dgsb, ndb ; dgsa := convert(a, base, 10) ; dgsb := convert(b, base, 10) ; if nops(dgsa) >= nops(dgsb) then ndb := nops(dgsb) ; [op(1..ndb, dgsa)] = dgsb ; else false; end if; end proc:
for i from 1 do if endswith(numtheory[sigma][2](i), i) then printf("%d, \n", i) ; end if; end do: # R. J. Mathar, May 30 2010


MATHEMATICA

(*returns true if a ends in b, false o.w.*) f[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; e = StringLength[c]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[2]] == e, r = True]]; r]; Select[Range[10^5], f[Divisor[2, # ], # ]] &]
Select[Range[10000], Mod[DivisorSigma[2, #], 10^IntegerLength[#]]==#&] (* Harvey P. Dale, Dec 09 2014 *)


CROSSREFS

Sequence in context: A244384 A290018 A323979 * A261375 A349758 A217740
Adjacent sequences: A067204 A067205 A067206 * A067208 A067209 A067210


KEYWORD

base,nonn


AUTHOR

Joseph L. Pe, Feb 19 2002


STATUS

approved



