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

1,4

Comments

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

Links

Table of n, a(n) for n=1..71.

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

Cf. A037916, A118914, A124010, A212171.

Sequence in context: A339306 A139393 A037916 * A292355 A262181 A309497

Adjacent sequences: A320387 A320388 A320389 * A320391 A320392 A320393

Keyword

nonn,easy,base

Author

M. F. Hasler, Oct 12 2018

Status

approved