A067207 Numbers k such that the digits of sigma_2(k) end in k.

1, 60, 81, 340, 7060

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

No additional terms < 3*10^9. - Sean A. Irvine, Dec 06 2023

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