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A275949 Number of distinct nonzero digits that occur multiple times in factorial base representation of n: a(n) = A056170(A275735(n)). 5
0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,42

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..40320

Index entries for sequences related to factorial base representation

FORMULA

a(n) = A056170(A275735(n)).

Other identities and observations. For all n >= 0.

a(n) = A275947(A225901(n)).

A275806(n) = A275948(n) + a(n).

a(n) <= A275964(n).

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 are no nonzero digits that are present multiple times, thus a(2) = 0.

For n=3 ("11") there is one distinct nonzero digit which occurs more than once, thus a(3) = 1.

For n=41 ("1221") there are two distinct nonzero digits ("1" and "2"), and both occur more than once, thus a(41) = 2.

For n=44 ( "1310") there are two distinct nonzero digits ("1" and "3"), but only the other (1) occurs more than once, thus a(44) = 1.

PROG

(Scheme) (define (A275949 n) (A056170 (A275735 n)))

(Python)

from sympy import prime, factorint

from operator import mul

import collections

def a056170(n):

    f = factorint(n)

    return sum([1 for i in f if f[i]!=1])

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 xrange(len(y))])

def a(n): return a056170(a275735(n))

print [a(n) for n in xrange(201)] # Indranil Ghosh, Jun 20 2017

CROSSREFS

Cf. A056170, A275735.

Cf. A265349 (indices of zeros), A265350 (of terms > 0).

Cf. also A007623, A225901, A275806, A275947, A275948, A275964.

Sequence in context: A116929 A059984 A046675 * A090418 A076754 A101659

Adjacent sequences:  A275946 A275947 A275948 * A275950 A275951 A275952

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Aug 15 2016

STATUS

approved

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Last modified November 19 02:01 EST 2018. Contains 317332 sequences. (Running on oeis4.)