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A038369
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Numbers k such that k = (product of digits of k) * (sum of digits of k).
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19
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OFFSET
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1,3
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COMMENTS
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The list is complete. Proof: One shows that the number of digits is at most 84 and then it is only necessary to consider numbers of the forms 2^i*3^j*7^k and 3^i*5^j*7^k. - David W. Wilson, May 16 2003
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LINKS
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Alan Beardon, S.P numbers, The Mathematical Gazette, 83(496), 25-32 (1999).
Eric Weisstein's World of Mathematics, Digit.
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FORMULA
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EXAMPLE
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144 belongs to the sequence because 1*4*4=16, 1+4+4=9 -> 16*9=144
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MATHEMATICA
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pdsdQ[n_]:=Module[{idn=IntegerDigits[n]}, (Total[idn]Times@@idn)==n]; Select[Range[0, 150], pdsdQ] (* Harvey P. Dale, Apr 23 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nice,nonn,fini,base,full
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AUTHOR
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STATUS
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approved
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