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A276075 a(1) = 0, a(n) = (e1*i1! + e2*i2! + ... + ez*iz!) for n = prime(i1)^e1 * prime(i2)^e2 * ... * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k). 15
0, 1, 2, 2, 6, 3, 24, 3, 4, 7, 120, 4, 720, 25, 8, 4, 5040, 5, 40320, 8, 26, 121, 362880, 5, 12, 721, 6, 26, 3628800, 9, 39916800, 5, 122, 5041, 30, 6, 479001600, 40321, 722, 9, 6227020800, 27, 87178291200, 122, 10, 362881, 1307674368000, 6, 48, 13, 5042, 722, 20922789888000, 7, 126, 27, 40322, 3628801, 355687428096000, 10, 6402373705728000, 39916801, 28, 6, 726, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Additive with a(p^e) = e * (PrimePi(p)!), where PrimePi(n) = A000720(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..120

FORMULA

a(1) = 0; for n > 1, a(n) = a(A028234(n)) + (A067029(n) * A000142(A055396(n))).

Other identities.

For all n >= 0:

a(A276076(n)) = n.

a(A002110(n)) = A007489(n).

a(A019565(n)) = A059590(n).

a(A206296(n)) = A276080(n).

a(A260443(n)) = A276081(n).

For all n >= 1:

a(A000040(n)) = n! = A000142(n).

a(A076954(n-1)) = A033312(n).

PROG

(Scheme, with memoization-macro definec)

(definec (A276075 n) (cond ((= 1 n) (- n 1)) (else (+ (* (A067029 n) (A000142 (A055396 n))) (A276075 (A028234 n))))))

(Python)

from sympy import factorint, factorial as f, primepi

def a(n):

    F=factorint(n)

    return 0 if n==1 else sum([F[i]*f(primepi(i)) for i in F])

print [a(n) for n in xrange(1, 121)] # Indranil Ghosh, Jun 21 2017

CROSSREFS

Cf. A000040, A000142, A000720, A002110, A007489, A019565, A028234, A033312, A055396, A059590, A067029, A076954, A206296, A260443, A276080, A276081.

Left inverse of A276076.

Cf. also A048675.

Sequence in context: A263673 A266479 A130712 * A130728 A276085 A092384

Adjacent sequences:  A276072 A276073 A276074 * A276076 A276077 A276078

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 18 2016

STATUS

approved

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Last modified September 24 22:31 EDT 2017. Contains 292441 sequences.