A161350 - OEIS

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A161350

Numbers with property that the digital sum times the product of the digits is a square.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 22, 30, 39, 40, 50, 60, 70, 80, 88, 90, 93, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 123, 130, 132, 140, 144, 150, 160, 170, 180, 189, 190, 198, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 213, 220

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OFFSET

1,2

COMMENTS

93 is in the list because (9+3)*(9*3) = 12*27 = 324 = 18^2.

LINKS

Table of n, a(n) for n=1..59.

MAPLE

a := proc (n) local nn, L: nn := convert(n, base, 10): L := nops(nn): if type(sqrt(add(nn[i], i = 1 .. L)*(product(nn[i], i = 1 .. L))), integer) = true then n else end if end proc: seq(a(n), n = 1 .. 220); # Emeric Deutsch, Jun 27 2009

PROG

(PARI) isok(n) = my(d=digits(n)); issquare(sumdigits(n)*prod(k=1, #d, d[k])); \\ Michel Marcus, Feb 14 2015

CROSSREFS

Cf. A007953 (sum of digits), A007954 (product of digits).

Sequence in context: A190219 A038367 A214958 * A342048 A108652 A140665

Adjacent sequences: A161347 A161348 A161349 * A161351 A161352 A161353

KEYWORD

nonn,base

AUTHOR

Claudio Meller, Jun 07 2009

STATUS

approved