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A275805 Indices of nonsquarefree terms in A275734; numbers with at least one digit slope (in their factorial base representation) with multiple nonzero digits. (See comments for the exact definition). 7
5, 11, 14, 15, 17, 19, 21, 22, 23, 29, 35, 38, 39, 41, 43, 45, 46, 47, 53, 54, 55, 56, 57, 58, 59, 62, 63, 65, 67, 69, 70, 71, 74, 75, 77, 80, 81, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 125, 131, 134, 135, 137, 139, 141, 142, 143, 149, 155 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n for which A008683(A275734(n)) = 0.

Numbers n for which A275811(n) > 1.

Numbers n in whose factorial base representation (A007623) there exists at least one pair of digit positions i_1 and i_2 with nonzero digits d_1 and d_2 such that (i_1 - d_1) = (i_2 - d_2).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to factorial base representation

EXAMPLE

For n=5, "21" in factorial base (A007623), the pair 2 (in position 2) and 1 (in position 1) satisfies the condition, as (2-2) = (1-1), thus 5 is included.

For n=55, "2101" in factorial base, the pair 2 (in position 4) and 1 (in position 3) satisfies the condition, as (4-2) = (3-1), thus 55 is included.

For n=67, "2301" in factorial base, the pair 3 (in position 3) and 1 (in position 1) satisfies the condition, as (3-3) = (1-1), thus 67 is included in the sequence.

PROG

(Scheme, with Antti Karttunen's IntSeq-library, two alternatives)

(define A275805 (ZERO-POS 1 1 (COMPOSE A008683 A275734)))

(define A275805 (MATCHING-POS 1 1 (lambda (n) (< 1 (A275811 n)))))

(Python)

from operator import mul

from sympy import prime, factorial as f, mobius

def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p

def a275732(n):

    x=str(a007623(n))[::-1]

    return 1 if n==0 or x.count("1")==0 else reduce(mul, [prime(i + 1) for i in xrange(len(x)) if x[i]=='1'])

def a257684(n):

    x=str(a007623(n))[:-1]

    y="".join([str(int(i) - 1) if int(i)>0 else '0' for i in x])[::-1]

    return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in xrange(len(y))])

def a(n): return 1 if n==0 else a275732(n)*a(a257684(n))

print [n for n in xrange(201) if mobius(a(n))==0] # Indranil Ghosh, Jun 19 2017

CROSSREFS

Complement: A275804.

Cf. A007623, A008683, A275734, A275811.

Cf. A275809 (a subsequence apart from its initial 0-term).

Subsequence of A115945.

Sequence in context: A073615 A275118 A275640 * A313993 A297251 A293834

Adjacent sequences:  A275802 A275803 A275804 * A275806 A275807 A275808

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Aug 10 2016

STATUS

approved

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)