A067343 -id:A067343 - cp's OEIS frontend

A067344 Sum of decimal digits of square of divisors of n equals sum of square of digits of n.

1, 21, 41, 120, 242, 312, 323, 401, 501, 1040, 1114, 1141, 1204, 1214, 1233, 1241, 1304, 1503, 2033, 2115, 2133, 2140, 2403, 3010, 3014, 3124, 3211, 3304, 3322, 4001, 4012, 4121, 4301, 4310, 5130, 10044, 10214, 10242, 10320, 10324, 11042, 11115

Offset: 1

Labos Elemer, Jan 16 2002

			n=51223, SquareSumDigit=25+1+4+4+9=43, Sigma[2,51223]=2623908580 with digit sum=43.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A067342, A067343, A007953, A001157.

Do[s=Apply[Plus, IntegerDigits[DivisorSigma[2, n]]]- Apply[Plus, IntegerDigits[n]^2]; If[Equal[s, 0], Print[n]], {n, 1, 10000}]
Select[Range[12000],Total[Flatten[IntegerDigits[#]^2]]== Total[ IntegerDigits[ DivisorSigma[2,#]]]&] (* Harvey P. Dale, Sep 12 2012 *)

A007953[A001157(n)]=A007953[n]^2

A226327 Sum of digits of n equals sum of digits of its antisigma (A024816).

Original entry on oeis.org

24, 46, 69, 78, 145, 147, 169, 177, 186, 198, 451, 459, 460, 474, 478, 495, 568, 586, 588, 618, 639, 667, 685, 738, 801, 838, 864, 865, 987, 1194, 1198, 1485, 1486, 1495, 1558, 1566, 1639, 1698, 1738, 1878, 1954, 1959, 2295, 2458, 2494, 2538, 2584, 2655, 2656

Offset: 1

Paolo P. Lava, Jun 04 2013

			For 2584 we have antisigma(2584) = 2584*(2584 + 1)/2 - sigma(2584) = 3334420 and 2 + 5 + 8 + 4 = 3 + 3 + 3 + 4 + 4 + 2 + 0 = 19.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A024816, A067343.

with(numtheory); SA:=proc(t) global v,z; v:=0; z:=t;
while z>0 do v:=v+(z mod 10); z:=trunc(z/10); od; v; end:
A226327:=proc(q) local n; for n from 1 to q do
if SA(n)=SA(n*(n+1)/2-sigma(n)) then print(n);
fi; od; end: A226327(10^4);

cp's OEIS Frontend

A067344 Sum of decimal digits of square of divisors of n equals sum of square of digits of n.

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