

A320390


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


1



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
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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: A258055 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



