A285329 a(n) = A013928(A007947(n)).

0, 1, 2, 1, 3, 4, 5, 1, 2, 6, 7, 4, 8, 9, 10, 1, 11, 4, 12, 6, 13, 14, 15, 4, 3, 16, 2, 9, 17, 18, 19, 1, 20, 21, 22, 4, 23, 24, 25, 6, 26, 27, 28, 14, 10, 29, 30, 4, 5, 6, 31, 16, 32, 4, 33, 9, 34, 35, 36, 18, 37, 38, 13, 1, 39, 40, 41, 21, 42, 43, 44, 4, 45, 46, 10, 24, 47, 48, 49, 6, 2, 50, 51, 27, 52, 53, 54, 14, 55, 18, 56, 29, 57, 58, 59, 4, 60, 9, 20, 6

Offset

1,3

Comments

For n > 1, a(n) gives the (one-based) index of the column where n is located in array A284311, or respectively, index of the row where n is in A284457. A008479 gives the other index.

Links

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

Formula

a(n) = A013928(A007947(n)).

Other identities. For all n >= 0:

If A008683(n) <> 0 [when n is squarefree, A005117], a(n) = A013928(n), otherwise a(n) = a(A285328(n)).

a(A019565(n)) = A064273(n).

Prog

(Scheme, with memoization-macro definec)
(definec (A285329 n) (if (not (zero? (A008683 n))) (A013928 n) (A285329 (A285328 n))))
(define (A285329 n) (A013928 (A007947 n)))
(Python)
from operator import mul
from sympy import primefactors
from sympy.ntheory.factor_ import core
from functools import reduce
def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n))
def a013928(n): return sum(1 for i in range(1, n) if core(i) == i)
print([a013928(a007947(n)) for n in range(1, 101)]) # Indranil Ghosh, Apr 18 2017
(Python)
from math import prod, isqrt
from sympy import primefactors, mobius
def A285329(n):
    m=prod(primefactors(n))-1
    return sum(mobius(k)*(m//k**2) for k in range(1, isqrt(m)+1)) # Chai Wah Wu, May 12 2024

Crossrefs

Cf. A008479 (the other index).

Cf. A005117, A007947, A008683, A013928, A019565, A064273, A087207, A285328.

Cf. array A284311 (A284457).

Sequence in context: A210040 A349385 A357310 * A289023 A085985 A331747

Adjacent sequences: A285326 A285327 A285328 * A285330 A285331 A285332

Keyword

nonn,changed

Author

Antti Karttunen, Apr 17 2017

Status

approved