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A038369 Numbers n such that n = (product of digits of n) * (sum of digits of n). 15
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

Table of n, a(n) for n=1..4.

A. Beardon, S.P numbers, The Mathematical Gazette, 83(496), 25-32 (1999). doi:10.2307/3618679.

E. Bussmann, S.P numbers in bases other than 10, The Mathematical Gazette, 85(503), 245-248 (2001). doi:10.2307/3622010.

K. McLean, There are only three S.P numbers!, The Mathematical Gazette, 83(496), 32-38 (1999). doi:10.2307/3618680.

S. Parameswaran, Numbers and their digits - a structural pattern, Note 81.24, The Mathematical Gazette, 81(491), 263-263 (1997). doi:10.2307/3619204.

Eric Weisstein's World of Mathematics, Sum-Product Number.

Eric Weisstein's World of Mathematics, Digit.

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

n = A007953(n) * A007954(n).

Cf. A066282.

Sequence in context: A007251 A219443 A230699 * A066282 A235809 A066176

Adjacent sequences:  A038366 A038367 A038368 * A038370 A038371 A038372

KEYWORD

nice,nonn,fini,base,full

AUTHOR

Felice Russo

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)