The On-Line Encyclopedia of Integer Sequences (OEIS)

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A322979

a(n) = Sum A009191(d) over the divisors d of n, where A009191(x) = gcd(x, A000005(x)), and A000005(x) gives the number of divisors of x.
(history; published version)

#10 by Susanna Cuyler at Mon Jan 07 11:11:20 EST 2019

STATUS

proposed

approved

#9 by Antti Karttunen at Sat Jan 05 15:01:48 EST 2019

STATUS

editing

proposed

#8 by Antti Karttunen at Sat Jan 05 13:19:05 EST 2019

LINKS

Antti Karttunen, <a href="/A322979/b322979.txt">Table of n, a(n) for n = 1..10080</a>

#7 by Antti Karttunen at Sat Jan 05 13:17:50 EST 2019

LINKS

Antti Karttunen, <a href="/A322979/a322979.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

#6 by Antti Karttunen at Sat Jan 05 13:10:55 EST 2019

NAME

a(n) = Sum A009191(d) over the divisors d of n, where A009191(x) = gcd(x, A000005(x)), and A000005 is (x) gives the number of divisors of nx.

#5 by Antti Karttunen at Sat Jan 05 13:10:13 EST 2019

NAME

a(n) = Sum A009191(d) over the divisors d of n, where A009191(x) = gcd(x, A000005(x)), where and A000005 is the number of divisors of n.

#4 by Antti Karttunen at Sat Jan 05 13:09:53 EST 2019

NAME

a(n) = Sum A009191(d) over the divisors d of n, where A009191(nx) = gcd(n, dx, A000005(n)x), and d(n) , where A000005 is the number of divisors of n (A000005).

#3 by Antti Karttunen at Sat Jan 05 13:08:00 EST 2019

NAME

a(n) = Sum A009191(d) over the divisors d of n, where A009191(n) = gcd(n, d(n)), and d(n) is the number of divisors of n (A000005).

#2 by Antti Karttunen at Sat Jan 05 13:06:56 EST 2019

NAME

allocated for Antti Karttunena(n) = Sum A009191(d) over the divisors d of n.

DATA

1, 3, 2, 4, 2, 6, 2, 8, 5, 6, 2, 13, 2, 6, 4, 9, 2, 15, 2, 9, 4, 6, 2, 25, 3, 6, 6, 9, 2, 12, 2, 11, 4, 6, 4, 31, 2, 6, 4, 21, 2, 12, 2, 9, 10, 6, 2, 28, 3, 9, 4, 9, 2, 18, 4, 21, 4, 6, 2, 33, 2, 6, 10, 12, 4, 12, 2, 9, 4, 12, 2, 55, 2, 6, 8, 9, 4, 12, 2, 32, 7, 6, 2, 33, 4, 6, 4, 21, 2, 30, 4, 9, 4, 6, 4, 42, 2, 9, 10, 13, 2, 12, 2, 21, 8

OFFSET

1,2

COMMENTS

Inverse Möbius transform of A009191.

FORMULA

a(n) = Sum_{d|n} A009191(d).

PROG

(PARI)

A009191(n) = gcd(n, numdiv(n));

A322979(n) = sumdiv(n, d, A009191(d));

CROSSREFS

Cf. A009191.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Jan 05 2019

STATUS

approved

editing

#1 by Antti Karttunen at Tue Jan 01 13:12:41 EST 2019

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved