|
|
A320390
|
|
Prime signature of n (sorted in decreasing order), concatenated.
|
|
2
|
|
|
0, 1, 1, 2, 1, 11, 1, 3, 2, 11, 1, 21, 1, 11, 11, 4, 1, 21, 1, 21, 11, 11, 1, 31, 2, 11, 3, 21, 1, 111, 1, 5, 11, 11, 11, 22, 1, 11, 11, 31, 1, 111, 1, 21, 21, 11, 1, 41, 2, 21, 11, 21, 1, 31, 11, 31, 11, 11, 1, 211, 1, 11, 21, 6, 11, 111, 1, 21, 11, 111, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
In the variant A037916, the exponents of the prime factorization are concatenated without being sorted first (i.e., rows of A124010).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = concatenation of row n of A212171.
|
|
EXAMPLE
|
For n = 1, the prime signature is the empty sequence, so the concatenation of its terms yields 0 by convention.
For n = 2 = 2^1, n = 3 = 3^1 and any prime p = p^1, the prime signature is (1), and concatenation yields a(n) = 1.
For n = 4 = 2^2, the prime signature is (2), and concatenation yields a(n) = 2.
For n = 6 = 2^1 * 3^1, the prime signature is (1,1), and concatenation yields a(n) = 11.
For n = 12 = 2^2 * 3^1 but also n = 18 = 2^1 * 3^2, the prime signature is (2,1) since exponents are sorted in decreasing order; concatenation yields a(n) = 21.
For n = 30 = 2^1 * 3^1 * 5^1, the prime signature is (1,1,1), and concatenation yields a(n) = 111.
For n = 3072 = 2^10 * 3^1, the prime signature is (10,1), and concatenation yields a(n) = 101. This is the first term with nondecreasing digits.
|
|
MATHEMATICA
|
{0}~Join~Array[FromDigits@ Flatten[IntegerDigits /@ FactorInteger[#][[All, -1]] ] &, 78, 2] (* Michael De Vlieger, Oct 13 2018 *)
|
|
PROG
|
(PARI) a(n)=fromdigits(vecsort(factor(n)[, 2]~, , 4)) \\ Except for multiples of 2^10, 3^10, etc.
(PARI) a(n)=eval(concat(apply(t->Str(t), vecsort(factor(n)[, 2]~, , 4)))) \\ Slower but correct for all n.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|