A153631 Numbers n such that n modulo (product of digits of n) = (sum of digits of n).

23, 29, 33, 39, 43, 49, 53, 59, 63, 69, 73, 79, 83, 89, 93, 99, 133, 136, 137, 192, 194, 195, 222, 223, 226, 229, 261, 263, 267, 313, 316, 331, 332, 333, 334, 336, 339, 391, 392, 397, 441, 443, 449, 621, 623, 661, 662, 663, 666, 669, 912, 914, 915, 931, 932

Offset

1,1

Comments

Do consecutive numbers like 136, 137 occur frequently? Do many primes appear in the sequence?

Numbers n such that the positive integer remainder of n/A007954(n) equals A007953(n). [R. J. Mathar, Jan 03 2009]

Links

B. D. Swan, Table of n, a(n) for n=1,...,20000

Example

For n = 83, (product of digits of n) = 24, (sum of digits of n) = 11 and 83 = 3*24 + 11.
For n = 93, (product of digits of n) = 27, (sum of digits of n) = 12 and 93 = 3*27 + 12.

Maple

sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: pd := proc (n) options operator, arrow: product(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if 0 < pd(n) and `mod`(n, pd(n)) = sd(n) then n else end if end proc: seq(a(n), n = 1 .. 1000); # Emeric Deutsch, Jan 02 2009
A007953 := proc(n) local i ; add(i, i=convert(n, base, 10)) ; end: A007954 := proc(n) local i ; mul(i, i=convert(n, base, 10)) ; end: for n from 1 to 1200 do if A007954(n) > 0 then if irem(n, A007954(n))= A007953(n) then printf("%d, ", n) ; fi; fi; od: # R. J. Mathar, Jan 03 2009

Crossrefs

Sequence in context: A277206 A214754 A344375 * A082943 A061754 A180066

Adjacent sequences: A153628 A153629 A153630 * A153632 A153633 A153634

Keyword

base,easy,nonn

Author

J. M. Bergot, Dec 29 2008

Extensions

Edited, corrected (93 inserted) and extended beyond a(21) by Klaus Brockhaus, Jan 06 2009

Corrected and extended by Emeric Deutsch and R. J. Mathar, Jan 02 2009

Status

approved