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A118490
Squares for which both the sum of the digits and the product of the digits is a triangular number.
0
0, 1, 100, 3025, 5041, 6400, 10000, 21025, 23104, 26569, 32041, 36100, 38809, 47089, 63001, 87616, 88804, 110224, 122500, 130321, 157609, 170569, 178084, 195364, 199809, 201601, 203401, 209764, 211600, 218089, 300304, 302500, 351649, 395641
OFFSET
1,3
EXAMPLE
26569 is in the sequence because (1) it is a square, (2) the sum of its digits is 2+6+5+6+9=28, (3) the product of its digits is 2*6*8*6*9=3240, (4) 28 and 3240 are both triangular numbers.
MATHEMATICA
trnos=Accumulate[Range[0, 1000]];
spdQ[n_]:=Module[{idn=IntegerDigits[n]}, MemberQ[trnos, Total[idn]]&&MemberQ[trnos, Times@@idn]]; Select[Range[0, 650]^2, spdQ] (* Harvey P. Dale, Mar 05 2011 *)
CROSSREFS
Cf. A000217.
Sequence in context: A250845 A200937 A112889 * A146310 A117685 A091134
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), May 05 2006
STATUS
approved