A272215 -id:A272215 - cp's OEIS frontend

A272216 Exponent of the power of 2 that divides A272215(n).

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

Offset: 1

David A. Corneth, Apr 22 2016

			As A272215(1336) = 3136 is of the form 2^6 * k where k is an odd integer, a(1336) = 6.

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

Cf. A272215.

A343750 Let S be the set of all numbers that can be obtained by permuting the digits of n (leading zeros can be omitted). Then a(n) is that element of S with the smallest number of divisors. In case of a tie, choose the smallest.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 13, 41, 15, 61, 17, 81, 19, 2, 21, 22, 23, 24, 25, 26, 27, 82, 29, 3, 13, 23, 33, 43, 53, 63, 37, 83, 39, 4, 41, 24, 43, 44, 45, 46, 47, 48, 49, 5, 15, 25, 53, 45, 55, 65, 57, 58, 59, 6, 61, 26, 63, 46, 65

Offset: 1

Ctibor O. Zizka, Apr 27 2021

a(x0..0) = x, a(x..x) = x..x, x from {1,...,9}.

			n = 125, S = {125, 152, 215, 251, 512, 521}. The elements 251 and 521 have the smallest number of divisors which equals 2. The smallest from elements 251 and 521 is 251, thus a(125) = 251.

Cf. A000005, A272215.

a[n_] := Module[{perm  = FromDigits /@ Permutations[IntegerDigits[n]], d}, d = DivisorSigma[0, perm]; Min @ perm[[Position[d, Min[d]] // Flatten]]]; Array[a, 65] (* Amiram Eldar, Apr 27 2021 *)

a(n) = my(d=digits(n), nb=#d, v=vector(nb!, k, fromdigits(vector(#d, i, d[numtoperm(nb, k)[i]]))), w=apply(numdiv, v)); vecmin(select(x->(numdiv(x)==vecmin(w)), v)); \\ Michel Marcus, Jan 24 2025

A380391 Numbers k such that A343750(k) != k.

Original entry on oeis.org

10, 12, 14, 16, 18, 20, 28, 30, 31, 32, 34, 35, 36, 38, 40, 42, 50, 51, 52, 54, 56, 60, 62, 64, 68, 70, 71, 72, 73, 74, 75, 76, 78, 80, 84, 85, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 114, 115, 116, 118, 119, 120

Offset: 1

Ctibor O. Zizka, Jan 23 2025

			k = 13: A343750(13) = 13, thus k = 13 is not in the sequence.
k = 14: A343750(14) = 41, thus k = 14 is a term.

Cf. A000005, A004719, A010785, A272215, A343750.

q[k_] := Module[{perm = FromDigits /@ Permutations[IntegerDigits[k]], d}, d = DivisorSigma[0, perm]; Min@ perm[[Position[d, Min[d]] // Flatten]] != k]; Select[Range[120], q] (* Amiram Eldar, Jan 24 2025 *)

cp's OEIS Frontend

A272216 Exponent of the power of 2 that divides A272215(n).

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A343750 Let S be the set of all numbers that can be obtained by permuting the digits of n (leading zeros can be omitted). Then a(n) is that element of S with the smallest number of divisors. In case of a tie, choose the smallest.

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A380391 Numbers k such that A343750(k) != k.

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