A243534 -id:A243534 - cp's OEIS frontend

A243543 Smallest number whose list of divisors contains n distinct digits (in base 10).

1, 2, 4, 6, 12, 18, 36, 72, 54, 108

Offset: 1

Jaroslav Krizek, Jun 19 2014

Finite sequence with 10 terms.

			a(9) = 54 because 54 is the smallest number whose list of divisors contains 9 distinct digits; the list of divisors of 54: (1, 2, 3, 6, 9, 18, 27, 54) contains 9 distinct digits (1, 2, 3, 4, 5, 6, 7, 8, 9).

Cf. Sequences of numbers n such that list of divisors of n contains k distinct digits: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050.

Cf. also A095048, A037278, A176558, A243360.

A256825 Numbers with digits in strictly decreasing order containing digit 1.

Original entry on oeis.org

1, 10, 21, 31, 41, 51, 61, 71, 81, 91, 210, 310, 321, 410, 421, 431, 510, 521, 531, 541, 610, 621, 631, 641, 651, 710, 721, 731, 741, 751, 761, 810, 821, 831, 841, 851, 861, 871, 910, 921, 931, 941, 951, 961, 971, 981, 3210, 4210, 4310, 4321, 5210, 5310, 5321

Offset: 1

Jaroslav Krizek, Apr 10 2015

a(n) = possible values of A256824(m) in increasing order where A256824(m) = reverse concatenation of distinct digits of all divisors of m in base 10.
There are precisely 512 terms. Maximal term is 9876543210.
Subsequence of A009995 (numbers with digits in strictly decreasing order).
See A256826 - the smallest number k such that A256824(k) = a(n).

			21 is in sequence because there are numbers m such that A256824(m) = 21 (for m = 2, 22, 121, 211, 2111, ...).

Jaroslav Krizek, Table of n, a(n) for n = 1..512 (complete list)

Cf. A009995, A095050, A243534, A256824, A256826.

[Row n = 1 … 1023; Column A: A(n) = A009995(n); Column B: B(n) =  =IF(FIND("1";A(n);1)>0;A(n)); Arrangement of column B]

lista(nn) = for (n=1, nn, if ((d = digits(n)) && ((sd=vecsort(d,,8))==Vecrev(d)) && vecsearch(sd, 1), print1(n, ", "))); \\ Michel Marcus, Apr 11 2015

A256826 a(n) = the smallest number k such that A256824(k) = A256825(n).

Original entry on oeis.org

1, 101, 2, 3, 41, 5, 61, 7, 181, 19, 202, 103, 23, 401, 4, 43, 505, 25, 15, 451, 601, 122, 163, 461, 1661, 107, 127, 37, 47, 157, 67, 1801, 281, 83, 1481, 5581, 1861, 187, 109, 29, 9, 149, 59, 619, 79, 89, 2003, 404, 403, 123, 10, 503, 115, 4051, 12451, 453

Offset: 1

Jaroslav Krizek, Apr 13 2015

A256824(n) = reverse concatenation of distinct digits of all divisors of n in base 10, A256825(n) = possible values of A256824(m) in increasing order.

Finite sequence with 512 terms. Maximal term is a(185) = 88511.

			a(11) = 202 because 202 is the smallest number k such that reverse concatenation of distinct digits of all divisors of k (i.e. 1, 2, 101, 202) in base 10 = A256824(k) = A256824(202) = A256825(11) = 210.

Jaroslav Krizek, Table of n, a(n) for n = 1..512 (complete list)

Cf. A009995, A095050, A243534, A256824, A256825.

A256826:=func; [A256826(n): n in[A256825(n)]];

A190223 Numbers all of whose divisors are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 15, 17, 21, 22, 23, 25, 31, 33, 35, 37, 51, 53, 55, 71, 73, 75, 77, 111, 113, 115, 121, 125, 127, 131, 137, 151, 155, 157, 173, 175, 211, 213, 217, 221, 223, 227, 231, 233, 251, 253, 257, 271, 275, 277, 311, 313, 317, 331, 337, 353

Offset: 1

Jaroslav Krizek, May 06 2011

Subset of A001742.

All terms are obviously odd except for 2 and numbers of the form 2*A004022(k). - Harvey P. Dale, May 28 2014 (corrected by Iain Fox, Sep 03 2020)

			Number 115 is in sequence because all divisors of 115 (1, 5, 23, 115) are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from G. C. Greubel)

Supersequence: A001742.

Cf. A004022, A243534.

ncnQ[n_]:=Module[{digs=Union[Flatten[IntegerDigits/@Divisors[n]]]}, Complement[ digs,{1,2,3,5,7}]=={}]; Select[ Range[ 400],ncnQ] (* Harvey P. Dale, May 28 2014 *)

is(k) = fordiv(k, d, if(setminus(vecsort(digits(d), , 8), [1, 2, 3, 5, 7]) != [], return(0))); 1 \\ Iain Fox, Dec 28 2017

More terms from Harvey P. Dale, May 28 2014

cp's OEIS Frontend

A243543 Smallest number whose list of divisors contains n distinct digits (in base 10).

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A256825 Numbers with digits in strictly decreasing order containing digit 1.

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A256826 a(n) = the smallest number k such that A256824(k) = A256825(n).

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A190223 Numbers all of whose divisors are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

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