OFFSET
1,4
COMMENTS
FORMULA
a(n) = concatenation of row n of A212171.
a(n) = a(A046523(n)). - David A. Corneth, Oct 13 2018
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
M. F. Hasler, Oct 12 2018
STATUS
approved