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 A153631 Numbers n such that n modulo (product of digits of n) = (sum of digits of n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A244077 A277206 A214754 * 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

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Last modified October 23 22:42 EDT 2019. Contains 328378 sequences. (Running on oeis4.)