A087142 -id:A087142 - cp's OEIS frontend

A051004 Numbers divisible both by their individual digits and by the sum of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 111, 112, 126, 132, 135, 144, 162, 216, 222, 224, 264, 288, 312, 315, 324, 333, 336, 396, 432, 444, 448, 555, 612, 624, 648, 666, 735, 777, 864, 888, 936, 999, 1116, 1122, 1128, 1164, 1212, 1224, 1236, 1296, 1332

Offset: 1

Eric W. Weisstein

No zero digits permitted. [Harvey P. Dale, Dec 18 2011]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Digit

Intersection of A005349 and A034838.

Cf. A038369, A087142.

a051004 n = a051004_list !! (n-1)
a051004_list =  [x | x <- a005349_list,
                     x == head (dropWhile (< x) a034838_list)]
-- Reinhard Zumkeller, Mar 03 2012

ddQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,0] && Divisible[ n,Total[idn]]&& And @@ Divisible[n,idn]]; Select[Range[1400],ddQ] (* Harvey P. Dale, Dec 18 2011 *)

Offset corrected by Reinhard Zumkeller, Mar 03 2012

A087141 Numbers divisible by the sum of their digits, but not by all their individual digits.

Original entry on oeis.org

10, 18, 20, 21, 27, 30, 40, 42, 45, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 114, 117, 120, 133, 140, 150, 152, 153, 156, 171, 180, 190, 192, 195, 198, 200, 201, 204, 207, 209, 210, 220, 225, 228, 230, 234, 240, 243, 247, 252, 261, 266, 270

Offset: 1

Reinhard Zumkeller, Aug 18 2003

			225 is in the sequence as 225 is divisible by 2 + 2 + 5 = 9 but not by 2 while 2 is a digit of 225. - _David A. Corneth_, Jan 28 2021

David A. Corneth, Table of n, a(n) for n = 1..10000

Intersection of A087140 and A005349.

Cf. A087142.

is(n) = { my(d = digits(n), sd = vecsum(d), s = Set(d)); if(sd != 0 && n % sd == 0, if(s[1] == 0, return(1) ); for(i = 1, #s, if(n % s[i] != 0, return(1) ) ); 0 ); 0 } \\ David A. Corneth, Jan 28 2021

def ok(n):
    d = list(map(int, str(n)))
    if n == 0 or n%sum(d): return False
    return 0 in d or any(n%di for di in set(d))
print([k for k in range(271) if ok(k)]) # Michael S. Branicky, Oct 18 2021

A337163 Numbers divisible by their individual digits, but not by the product of their digits.

Original entry on oeis.org

22, 33, 44, 48, 55, 66, 77, 88, 99, 122, 124, 126, 155, 162, 168, 184, 222, 244, 248, 264, 288, 324, 333, 336, 366, 396, 412, 424, 444, 448, 488, 515, 555, 636, 648, 666, 728, 777, 784, 824, 848, 864, 888, 936, 999, 1122, 1124, 1128, 1144, 1155, 1164, 1222

Offset: 1

Bernard Schott, Jan 28 2021

The sequence is infinite. For example, all numbers of the form ((10^n-1)/9)*(10^2)+24 are terms for n > 0. The numbers of this form will never be divisible by 8 but they will always be divisible by 1, 2 and 4. Also there are infinitely many terms any three of whose consecutive digits are distinct, for example, concatenations of 124. Are there infinitely many terms which don't consist of periodically repeating substrings? - Metin Sariyar, Jan 28 2021

Every repdigit non-repunit with at least 2 digits is a term. - Bernard Schott, Jan 28 2021

			48 is divisible by 4 and 8, but 48 is not divisible by 4*8 = 32, so 48 is a term.
128 is divisible by 1, 2 and 8, and 128 is divisible by 1*2*8 = 16 with 128 = 16*8, so 128 is not a term.

David A. Corneth, Table of n, a(n) for n = 1..10000

Intersection of A034838 and A188643.
Cf. A087142 (similar, with sum).
Cf. A087141, A285271.

q[n_] := AllTrue[(digits = IntegerDigits[n]), # > 0 && Divisible[n, #] &] && !Divisible[n, Times @@ digits]; Select[Range[1000], q] (* Amiram Eldar, Jan 28 2021 *)

isok(n) = my(d=digits(n)); if (vecmin(d), for (i=1, #d, if (n % d[i], return(0))); (n % vecprod(d))); \\ Michel Marcus, Jan 28 2021

More terms from Michel Marcus, Jan 28 2021

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A051004 Numbers divisible both by their individual digits and by the sum of their digits.

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A087141 Numbers divisible by the sum of their digits, but not by all their individual digits.

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A337163 Numbers divisible by their individual digits, but not by the product of their digits.

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Mathematica

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Extensions