A051004 -id:A051004 - cp's OEIS frontend

A342262 Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 24, 30, 36, 40, 50, 60, 70, 80, 90, 100, 102, 110, 111, 112, 120, 132, 135, 140, 144, 150, 200, 210, 216, 220, 224, 240, 300, 306, 312, 315, 360, 400, 432, 480, 500, 510, 540, 550, 600, 612, 624, 630, 700, 735, 800, 900, 1000, 1002, 1008

Offset: 1

Bernard Schott, Mar 27 2021

Equivalently, Niven numbers that are divisible by the product of their nonzero digits. A Niven number (A005349) is a number that is divisible by the sum of its digits.
Niven numbers without zero digit that are divisible by the product of their digits are in A038186.
Differs from super Niven numbers, the first 16 terms are the same, then A328273(17) = 48 while a(17) = 50.
This sequence is infinite since if m is a term, then 10*m is another term.

			The product of the nonzero digits of 306 =  3*6 = 18, and 306 divided by 18 = 17. The sum of the digits of 306 = 3 + 0 + 6 = 9, and 306 divided by 9 = 34. Thus 306 is a term.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Intersection of A005349 and A055471.
Supersequence of A038186.
Cf. A051004, A328273, A342650.

q[n_] := And @@ Divisible[n, {Times @@ (d = Select[IntegerDigits[n], # > 0 &]), Plus @@ d}]; Select[Range[1000], q] (* Amiram Eldar, Mar 27 2021 *)
Select[Range[1200],Mod[#,Times@@(IntegerDigits[#]/.(0->1))]== Mod[#,Total[ IntegerDigits[#]]]==0&] (* Harvey P. Dale, Sep 26 2021 *)

isok(m) = my(d=select(x->(x!=0), digits(m))); !(m % vecprod(d)) && !(m % vecsum(d)); \\ Michel Marcus, Mar 27 2021

Example clarified by Harvey P. Dale, Sep 26 2021

A342650 Numbers divisible both by their nonzero individual digits and by the sum of their digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 24, 30, 36, 40, 48, 50, 60, 70, 80, 90, 100, 102, 110, 111, 112, 120, 126, 132, 135, 140, 144, 150, 162, 200, 204, 210, 216, 220, 222, 224, 240, 264, 280, 288, 300, 306, 312, 315, 324, 330, 333, 336, 360, 396, 400, 408, 420, 432, 440, 444, 448, 480, 500

Offset: 1

Bernard Schott, Mar 18 2021

Equivalently, Niven numbers that are divisible by their nonzero digits. A Niven number (A005349) is a number that is divisible by the sum of its digits.
Niven numbers without zero digit that are divisible by their individual digits are in A051004.
Differs from super Niven numbers, the first 25 terms are the same, then A328273(26) = 120 while a(26) = 111.
This sequence is infinite since if m is a term, then 10*m is another term.

			102 is divisible by its nonzero digits 1 and 2, and 102 is also divisible by the sum of its digits 1 + 0 + 2 = 3, then 102 is a term.

Intersection of A002796 and A005349.
Supersequence of A051004.
Cf. A034838, A328273.

q[n_] := AllTrue[(d = IntegerDigits[n]), # == 0 || Divisible[n, #] &] && Divisible[n, Plus @@ d]; Select[Range[500], q] (* Amiram Eldar, Mar 18 2021 *)

isok(m) = if (!(m % sumdigits(m)), my(d=select(x->(x>0), Set(digits(m)))); setintersect(d, divisors(m)) == d); \\ Michel Marcus, Mar 18 2021

A228017 Numbers n divisible by the sum of any k-subset of digits of n with k >= 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48

Offset: 1

Derek Orr, Aug 02 2013

No additional terms less than 20000000. - T. D. Noe, Aug 14 2013

Terms > 9 must be even since any pair of digits has an even subset. Since terms must also be zeroless, they cannot be divisible by 5, which means no further terms could have 5 or more digits by the Pigeonhole Principle. Therefore, this sequence is complete. - Charlie Neder, May 31 2019

			48 is here because 48 is divisible by 4, 8, and 4+8.

Subset of A051004 and of A346535.

okQ[n_] := Module[{s = Total /@ Rest[Subsets[IntegerDigits[n]]]}, ! MemberQ[s, 0] && And @@ IntegerQ /@ (n/s)]; Select[Range[10000], okQ] (* T. D. Noe, Aug 14 2013 *)

cp's OEIS Frontend

A342262 Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).

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A342650 Numbers divisible both by their nonzero individual digits and by the sum of their digits.

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A228017 Numbers n divisible by the sum of any k-subset of digits of n with k >= 1.

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Mathematica