A320390 Prime signature of n (sorted in decreasing order), concatenated.

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

Offset: 1

Author

M. F. Hasler, Oct 12 2018

Keywords

• nonn
• easy
• base

Comments

In the variant A037916, the exponents of the prime factorization are concatenated without being sorted first (i.e., rows of A124010).

Examples

			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.
		

Crossrefs

Cf. A037916, A118914, A124010, A212171.

Programs

Mathematica

{0}~Join~Array[FromDigits@ Flatten[IntegerDigits /@ FactorInteger[#][[All, -1]] ] &, 78, 2] (* Michael De Vlieger, Oct 13 2018 *)

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.

Formula

a(n) = concatenation of row n of A212171.

a(n) = a(A046523(n)). - David A. Corneth, Oct 13 2018