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A287170 a(n) = number of runs of consecutive prime numbers among the prime divisors of n. 5
0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

a(n) = 0 iff n = 1.

a(n) = 1 iff n belongs to A073491.

a(p) = 1 for any prime p.

a(A002110(n)) = 1 for any n > 0.

a(n!) = 1 for any n > 1.

a(A066205(n)) = n for any n > 0.

a(n) = a(A007947(n)) for any n > 0.

a(n) = a(A003961(n)) for any n > 0.

a(n*m) <= a(n) + a(m) for any n > 0 and m > 0.

Each number n can be uniquely represented as a product of a(n) distinct terms from A073491; this representation is minimal relative to the number of terms.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of the first terms

Rémy Sigrist, Scatterplot of the ordinal transform of the first 1000000 terms

FORMULA

a(n) = A069010(A087207(n))

EXAMPLE

See illustration of the first terms in the Links section.

PROG

(PARI) a(n) = my (f=factor(n)); if (#f~==0, return (0), return (#f~ - sum(i=1, #f~-1, if (primepi(f[i, 1])+1 == primepi(f[i+1, 1]), 1, 0))))

(Python)

from sympy import factorint, primepi

def a087207(n):

    f=factorint(n)

    return sum([2**primepi(i - 1) for i in f])

def a069010(n): return sum(1 for d in bin(n)[2:].split('0') if len(d)) # this function from Chai Wah Wu

def a(n): return a069010(a087207(n)) # Indranil Ghosh, Jun 06 2017

CROSSREFS

Cf. A002110, A003961, A007947, A066205, A069010, A073491, A087207.

Sequence in context: A331284 A331591 A003649 * A216784 A256067 A256554

Adjacent sequences:  A287167 A287168 A287169 * A287171 A287172 A287173

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jun 04 2017

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)