A075047
Numbers k whose prime factorization contains the same digits as k.
Original entry on oeis.org
25, 121, 471663, 931225, 4473225, 6953931, 7301441, 10713728, 13246317, 17332133, 19367424, 34706961, 36310761, 54363717, 68714219, 73553125, 73641071, 74390183, 93478133, 102712448, 102941361, 109502361, 113162997, 115521875, 120934784, 134179011, 134381673, 134472875, 135478125
Offset: 1
25 = 5^2 and 121 = 11^2 are terms.
The term 1971753273 -> 1,9,7,1,7,5,3,2,7,3 -> 1,1,2,3,3,5,7,7,7,9 is in the sequence because its factorization is 3^7*7^1*37^1*59^2 -> 3,7,7,1,3,7,1,5,9,2 -> 1,1,2,3,3,5,7,7,7,9 and this coincides with the digits of the term itself. - _Robert G. Wilson v_, Jun 06 2014
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fQ[n_] := Sort@ IntegerDigits@ n == Sort@ Flatten@ IntegerDigits@ FactorInteger@ n; k = 1; lst = {}; While[k < 100000001, If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Jun 05 2014 *)
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isok(n, b=10) = {f = factor(n); v = []; for (i=1, #f~, v = concat(v, digits(f[i,1], b)); v = concat(v, digits(f[i,2], b));); vecsort(v) == vecsort(digits(n, b));} \\ Michel Marcus, Jul 14 2015
A074211
Composites which use less than all of their digits in their prime factorization.
Original entry on oeis.org
1024, 1331, 3645, 4375, 10201, 14641, 15625, 17253, 19321, 19683, 24389, 32805, 37179, 49375, 74431, 78125, 117649, 131072, 137216, 137842, 147833, 159375, 161051, 161792, 167042, 170471, 205379, 214369, 214375, 234375, 239872, 249318
Offset: 1
A074237
Composites which use more than all their digits in their prime factorization.
Original entry on oeis.org
95, 132, 225, 232, 312, 322, 324, 325, 326, 423, 432, 731, 735, 912, 973, 995, 1111, 1212, 1233, 1275, 1292, 1972, 2132, 2312, 2737, 2793, 2994, 3171, 3192, 3210, 3211, 3212, 3243, 3315, 3472, 3792, 3992, 4172, 4212, 4341, 4371, 5192, 5216, 5271, 5283
Offset: 1
A353059
Integers k such that the prime factorization of k uses digits from a proper subset of the digits of k.
Original entry on oeis.org
143, 187, 341, 351, 451, 671, 781, 1023, 1024, 1057, 1207, 1243, 1324, 1352, 1372, 1375, 1379, 1703, 1982, 2139, 2176, 2189, 2317, 2321, 2510, 2519, 2816, 3051, 3125, 3159, 3375, 3421, 3641, 3861, 4232, 5102, 5210, 6182, 6272, 7819, 8197, 8921, 9251, 9317, 9481, 9531
Offset: 1
143 = 11^1 * 13^1: the number itself uses digits 1, 3, and 4, while the prime factorization uses the subset of digits: 1 and 3. Thus, 143 is in this sequence.
25 = 5^2. Both the number and the prime factorization use the same set of digits. Thus, 25 is not in this sequence.
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Select[Range[10000], SubsetQ[Union[IntegerDigits[#]], Union[Flatten[IntegerDigits[FactorInteger[#]]]]] && Length[Union[IntegerDigits[#]]] > Length[Union[Flatten[IntegerDigits[FactorInteger[#]]]]] &]
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from sympy import factorint
def ok(n): return set("".join(str(p)+str(e) for p, e in factorint(n).items())) < set(str(n))
print([k for k in range(2, 9999) if ok(k)]) # Michael S. Branicky, Apr 20 2022
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