A254524 -id:A254524 - cp's OEIS frontend

A286558 Ordinal transform of A005811.

1, 1, 1, 2, 2, 1, 3, 3, 4, 2, 1, 3, 5, 4, 6, 4, 7, 5, 2, 6, 3, 1, 4, 7, 8, 8, 5, 9, 9, 10, 10, 5, 11, 11, 6, 12, 7, 2, 8, 13, 9, 3, 1, 4, 10, 5, 11, 14, 12, 15, 12, 16, 13, 6, 14, 17, 13, 18, 15, 19, 14, 20, 15, 6, 16, 21, 16, 22, 17, 7, 18, 23, 19, 8, 2, 9, 20, 10, 21, 24, 22, 11, 3, 12, 4, 1, 5, 13, 23, 14, 6, 15, 24, 16, 25, 25, 17, 26, 26, 27, 27, 17, 28, 28

Offset: 0

Antti Karttunen, May 21 2017

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A005811.

Cf. A263017, A254524, A286478, A286554 for similar sequences.

A326307 a(n) is the index of n in the ordered list of the numbers with the same digits as n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2

Offset: 0

David A. Corneth, Oct 17 2019

Ordinal transform of A328447.

			a(321) = 6 as 321 is the sixth number made of the digits [1, 2, 3]. The five smaller numbers having these digits are 123, 132, 213, 231, 312.

David A. Corneth, Table of n, a(n) for n = 0..9999
David A. Corneth, PARI program

Cf. A179239, A254524, A328447.

PARI
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see Corneth link
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{ o = vector(100); for (n=0, 87, print1 (o[1+fromdigits(vecsort(digits(n,base=10),,4),base)]++ ", ")) } \\ Rémy Sigrist, Oct 17 2019

A326307(n,D=Vecsmall(digits(n)),c=1)={forperm(vecsort(D),d, d==D&&break; d[1]&&c++);c} \\ M. F. Hasler, May 19 2021

from collections import Counter
from itertools import count, islice
def agen(): # generator of terms
    digmultisetcount = Counter()
    for n in count(0):
        key = "".join(sorted(str(n)))
        digmultisetcount[key] += 1
        yield digmultisetcount[key]
print(list(islice(agen(), 88))) # Michael S. Branicky, Jan 30 2025

a(A179239(n)) = 1.

a(10+n) = A007953(9*n)/9 (A007953 = sum of digits) for 0 < n < 91, but a(101) = 1 while A007953(9*91)/9 = 2. - M. F. Hasler, May 19 2021

Edited by N. J. A. Sloane, Oct 24 2019

A335286 n is the a(n)-th positive integer having its sequence of exponents in canonical prime factorization.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 4, 1, 2, 2, 5, 1, 6, 3, 4, 1, 7, 1, 8, 2, 5, 6, 9, 1, 3, 7, 2, 3, 10, 1, 11, 1, 8, 9, 10, 1, 12, 11, 12, 2, 13, 2, 14, 4, 5, 13, 15, 1, 4, 2, 14, 6, 16, 1, 15, 3, 16, 17, 17, 1, 18, 18, 7, 1, 19, 3, 19, 8, 20, 4, 20, 1, 21, 21, 3, 9, 22, 5, 22, 2

Offset: 1

David A. Corneth, May 30 2020

			a(14) = 3 as 14 has prime signature [1, 1] and it's the third positive integer having that prime signature, after 6 and 10.

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

Cf. A046523, A064839, A071364, A120426, A254524.

p:= proc() 0 end:
a:= proc(n) option remember; local t; a(n-1); t:=
      (l-> mul(ithprime(i)^l[i][2], i=1..nops(l)
       ))(sort(ifactors(n)[2])); p(t):= p(t)+1
    end: a(0):=0:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 01 2020

A071364[n_] := If[n == 1, 1, With[{f = FactorInteger[n]}, Times @@ (Prime[Range[Length[f]]]^f[[All, 2]])]];
Module[{b}, b[_] = 0;
a[n_] := With[{t = A071364[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

first(n) = { my(m = Map(), res = vector(n)); for(i = 1, n, c = factor(i)[,2]; if(mapisdefined(m, c), res[i] = mapget(m, c) + 1; mapput(m, c, res[i]) , res[i] = 1; mapput(m, c, 1) ) ); res }

Ordinal transform of A071364. - Alois P. Heinz, Jun 01 2020

A263019 If n is the i-th positive integer with digital sum j, then a(n) is the j-th positive integer with digital sum i.

Original entry on oeis.org

1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 2, 11, 20, 101, 110, 200, 1001, 1010, 1100, 1000000000, 12, 21, 30, 102, 111, 120, 201, 210, 2000, 10000000000, 22, 31, 40, 103, 112, 121, 130, 300, 10001, 100000000000, 32, 41, 50, 104, 113, 122

Offset: 1

Paul Tek, Oct 07 2015

Digital sum is given by A007953.
This is a self-inverse permutation of the natural numbers, with fixed points A081927.
A007953(n) = A081927(a(n)) for any n>0.
A081927(n) = A007953(a(n)) for any n>0.
a(A051885(n)) = 10^(n-1) for any n>0.
a(10^(n-1)) = A051885(n) for any n>0.

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, PERL program for this sequence

Cf. A007953, A051885, A081927, A254524, A263018.

a(n) = {j = sumdigits(n); v = vector(n, k, sumdigits(k)); i = #select(x->x==j, v); nb = 0; k = 0; while(nb != j, k++; if (sumdigits(k) == i, nb++)); k;} \\ Michel Marcus, Oct 16 2015

A338505 Number of positive integers less than n with the same product of decimal digits as n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 3, 2, 1, 0, 1, 0, 0, 0, 3, 3, 3, 2, 1, 0, 1, 0, 0, 0, 4, 2, 1, 1, 1, 0, 0, 0, 0, 0, 5, 4, 3, 2, 2, 1, 1, 0, 0, 0, 6, 2, 1, 1, 1, 1, 1, 0, 0, 0, 7, 4, 2, 3, 1, 1, 1, 1, 0, 0, 8

Offset: 1

Ilya Gutkovskiy, Oct 31 2020

			a(22) = 2 because A007954(22) = 4 and also A007954(4) = A007954(14) = 4.

Cf. A007954, A138471, A254524.

Table[Length[Select[Range[n - 1], Times @@ IntegerDigits@# == Times @@ IntegerDigits@n &]], {n, 90}]

a(n)={my(t=vecprod(digits(n))); sum(k=1, n-1, vecprod(digits(k))==t)} \\ Andrew Howroyd, Oct 31 2020

a(n) = |{0 < j < n : A007954(j) = A007954(n)}|.

Definition clarified by Ilya Gutkovskiy, Apr 14 2022

A340294 a(n) = pi(A340063(n)) = A000720(A340063(n)) for prime A340063(n) and otherwise k such that A340063 is the k-th positive integer having its digitsum.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 4, 1, 5, 5, 6, 2, 4, 7, 6, 8, 3, 5, 9, 1, 10, 7, 11, 2, 6, 12, 3, 13, 8, 14, 4, 7, 15, 2, 16, 3, 17, 9, 18, 4, 8, 19, 5, 20, 10, 21, 4, 22, 5, 9, 23, 5, 24, 1, 25, 6, 10, 26, 11, 27, 7, 28, 12, 29, 7, 11, 30, 1, 6, 31, 8, 32, 6, 33, 13, 34, 2

Offset: 1

David A. Corneth, Jan 03 2021

			a(17) = 8 as A340063(17) = 19 which is the 8th prime.
a(25) = 2 as A340063(25) = 14 which is composite and 14 is the second positive integer with digitsum 5.

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

Cf. A000720, A254524, A340063.

A357526 Number of nonnegative integers less than n with the same product of the nonzero decimal digits as n.

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 0, 0, 0, 0, 0, 2, 3, 3, 2, 1, 0, 1, 0, 0, 0, 3, 4, 3, 2, 1, 0, 1, 0, 0, 0, 2, 3, 1, 1, 1, 0, 0, 0, 0, 0, 4, 5, 3, 2, 2, 1, 1, 0, 0, 0, 2, 3, 1, 1, 1, 1, 1, 0, 0, 0, 4, 5, 2, 3, 1, 1, 1, 1, 0, 0, 3

Offset: 0

Ilya Gutkovskiy, Oct 02 2022

			a(1) = 1 because A051801(1) = 1 and also A051801(0) = 1.
a(21) = 3 because A051801(21) = 2 and also A051801(2) = A051801(12) = A051801(20) = 2.

Ilya Gutkovskiy, Scatterplot of a(n) up to n=10000

Cf. A051801, A138471, A254524, A338505.

Table[Length[Select[Range[0, n - 1], Times @@ DeleteCases[IntegerDigits[#], 0] == Times @@ DeleteCases[IntegerDigits[n], 0] &]], {n, 0, 90}]

a(n) = |{j < n : A051801(j) = A051801(n)}|.

A385957 Prime(n) is the a(n)-th prime having its distinct digits.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 5, 6, 3, 7, 3, 1, 1, 2, 1, 1, 4, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 3, 1, 1

Offset: 1

David A. Corneth, Jul 13 2025

			a(1) = 1 as prime(1) = 2 is the first prime having its distinct digits {2}.
a(11) = 2 as prime(11) = 31 is the second prime having its disitinct digits {1, 3} (the first is 13).
a(32) = 4 as prime(32) = 131 is the fourth prime having its distinct digits {1, 3} (the first three are 13, 31 and 113).

David A. Corneth, Table of n, a(n) for n = 1..10000
David A. Corneth, PARI program
Michael De Vlieger, Scatterplot of a(n), n = 1..10^6.

Cf. A086066, A254524, A385776.

Block[{c, f, p}, c[] := 0; f[x] := Union@ IntegerDigits[x]; Reap[Do[p = Prime[n]; Sow[++c[f[p] ] ], {n, 120}] ][[-1, 1]] ] (* Michael De Vlieger, Jul 13 2025 *)

PARI
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\\ See Corneth link
```

cp's OEIS Frontend

A286558 Ordinal transform of A005811.

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A326307 a(n) is the index of n in the ordered list of the numbers with the same digits as n.

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A335286 n is the a(n)-th positive integer having its sequence of exponents in canonical prime factorization.

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A263019 If n is the i-th positive integer with digital sum j, then a(n) is the j-th positive integer with digital sum i.

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PARI

A338505 Number of positive integers less than n with the same product of decimal digits as n.

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PARI

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A340294 a(n) = pi(A340063(n)) = A000720(A340063(n)) for prime A340063(n) and otherwise k such that A340063 is the k-th positive integer having its digitsum.

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A357526 Number of nonnegative integers less than n with the same product of the nonzero decimal digits as n.

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Mathematica

Formula

A385957 Prime(n) is the a(n)-th prime having its distinct digits.

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Mathematica