

A275806


a(n) = number of distinct nonzero digits in factorial base representation of n.


11



0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 4, 1
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OFFSET

0,6


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..40320
Index entries for sequences related to factorial base representation


FORMULA

a(n) = A001221(A275735(n)).
a(n) = A060502(A225901(n)).
Other identities. For all n >= 0:
a(n) = a(A153880(n)) = a(A255411(n)). [The shiftoperations do not change the number of distinct nonzero digits.]
a(A265349(n)) = A060130(A265349(n)).
a(A000142(n)) = 1.
a(A033312(n)) = n1, for all n >= 1.


EXAMPLE

For n=0, with factorial base representation (A007623) also 0, there are no nonzero digits, thus a(0) = 0.
For n=2, with factorial base representation "10", there is one distinct nonzero digit, thus a(2) = 1.
For n=3, with factorial base representation "11", there is just one distinct nonzero digit, thus a(3) = 1.
For n=44, with factorial base representation "1310", there are two distinct nonzero digits ("1" and "3"), thus a(44) = 2.


PROG

(Scheme) (define (A275806 n) (A001221 (A275735 n)))
(Python)
from sympy import prime, primefactors
from operator import mul
import collections
def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p
def a275735(n):
y=collections.Counter(map(int, list(str(a007623(n)).replace("0", "")))).most_common()
return 1 if n==0 else reduce(mul, [prime(y[i][0])**y[i][1] for i in range(len(y))])
def a(n): return len(primefactors(a275735(n)))
print [a(n) for n in range(201)] # Indranil Ghosh, Jun 20 2017


CROSSREFS

Cf. A000142, A001221, A007623, A033312, A060130, A060502, A225901, A265349, A275735.
Cf. also A153880, A255411.
Sequence in context: A053797 A254011 A002635 * A228369 A296773 A108244
Adjacent sequences: A275803 A275804 A275805 * A275807 A275808 A275809


KEYWORD

nonn,base,changed


AUTHOR

Antti Karttunen, Aug 11 2016


STATUS

approved



