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A038369 Numbers k such that k = (product of digits of k) * (sum of digits of k). 19
0, 1, 135, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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
LINKS
Alan Beardon, S.P numbers, The Mathematical Gazette, 83(496), 25-32 (1999).
Alan Beardon, Sums and Products of Digits and SP Numbers, NRICH, University of Cambridge, 1998.
Alan Beardon, Recent Developments on S.P. Numbers, NRICH, University of Cambridge, 1998-2011.
E. Bussmann, S.P numbers in bases other than 10, The Mathematical Gazette, 85(503), 245-248 (2001).
K. McLean, There are only three S.P numbers!, The Mathematical Gazette, 83(496), 32-38 (1999).
S. Parameswaran, Numbers and their digits - a structural pattern, Note 81.24, The Mathematical Gazette, 81(491), 263-263 (1997).
Eric Weisstein's World of Mathematics, Sum-Product Number.
Eric Weisstein's World of Mathematics, Digit.
FORMULA
a(n) = A007953(a(n)) * A007954(a(n)).
EXAMPLE
144 belongs to the sequence because 1*4*4=16, 1+4+4=9 -> 16*9=144
MATHEMATICA
pdsdQ[n_]:=Module[{idn=IntegerDigits[n]}, (Total[idn]Times@@idn)==n]; Select[Range[0, 150], pdsdQ] (* Harvey P. Dale, Apr 23 2011 *)
PROG
(PARI) is(n)=my(d=digits(n)); factorback(d)*vecsum(d)==n \\ Charles R Greathouse IV, Feb 06 2017
CROSSREFS
Sequence in context: A230699 A335950 A355002 * A066282 A235809 A066176
KEYWORD
nice,nonn,fini,base,full
AUTHOR
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)