A378547 -id:A378547 - cp's OEIS frontend

A378546 a(n) is the sum of the divisors d of n for which A083345(n/d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

1, 2, 3, 4, 5, 6, 7, 8, 10, 10, 11, 13, 13, 14, 16, 17, 17, 20, 19, 21, 22, 22, 23, 26, 26, 26, 30, 29, 29, 32, 31, 34, 34, 34, 36, 43, 37, 38, 40, 42, 41, 44, 43, 45, 53, 46, 47, 55, 50, 52, 52, 53, 53, 60, 56, 58, 58, 58, 59, 72, 61, 62, 73, 68, 66, 68, 67, 69, 70, 72, 71, 86, 73, 74, 83, 77, 78, 80, 79, 89, 91

Offset: 1

Antti Karttunen, Nov 30 2024

nonn

Dirichlet convolution of A000027 with A369001.

Dirichlet convolution of A000010 (Euler phi) with A378444.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000010, A000027, A000203, A083345, A369001, A378444, A378547.

Cf. also A378544, A378545.

A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369001(n) = !(A083345(n)%2);
A378546(n) = sumdiv(n,d,d*A369001(n/d));

a(n) = Sum_{d|n} A369001(n/d)*d.
a(n) = Sum_{d|n} A000010(n/d)*A378444(d).
a(n) = A000203(n) - A378547(n).

A378543 Sum of divisors d of n such that n/d has an odd number of prime factors (counted with multiplicity).

Original entry on oeis.org

0, 1, 1, 2, 1, 5, 1, 5, 3, 7, 1, 11, 1, 9, 8, 10, 1, 16, 1, 15, 10, 13, 1, 25, 5, 15, 10, 19, 1, 32, 1, 21, 14, 19, 12, 35, 1, 21, 16, 35, 1, 42, 1, 27, 25, 25, 1, 51, 7, 36, 20, 31, 1, 50, 16, 45, 22, 31, 1, 72, 1, 33, 31, 42, 18, 62, 1, 39, 26, 60, 1, 80, 1, 39, 41, 43, 18, 72, 1, 71, 30, 43, 1, 94, 22, 45, 32, 65

Offset: 1

Antti Karttunen, Dec 01 2024

nonn

Agrees with A378549 on odd n.
Dirichlet convolution of A000027 with A066829.
Dirichlet convolution of A000010 (Euler phi) with A056924.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sums of divisors.

Cf. A000010, A000027, A000203, A056924, A066829, A378542.

Cf. also A378547, A378549.

A378543(n) = sumdiv(n,d,d*!!(bigomega(n/d)%2));

a(n) = Sum_{d|n} A066829(n/d)*d.
a(n) = Sum_{d|n} A000010(n/d)*A056924(d).
a(n) = A000203(n) - A378543(n).

A378549 Sum of divisors d of n such that n/d is not an odd number with an even number of prime factors (counted with multiplicity).

Original entry on oeis.org

0, 1, 1, 3, 1, 6, 1, 7, 3, 8, 1, 16, 1, 10, 8, 15, 1, 19, 1, 22, 10, 14, 1, 36, 5, 16, 10, 28, 1, 40, 1, 31, 14, 20, 12, 51, 1, 22, 16, 50, 1, 52, 1, 40, 25, 26, 1, 76, 7, 41, 20, 46, 1, 60, 16, 64, 22, 32, 1, 104, 1, 34, 31, 63, 18, 76, 1, 58, 26, 72, 1, 115, 1, 40, 41, 64, 18, 88, 1, 106, 30, 44, 1, 136, 22, 46, 32

Offset: 1

Antti Karttunen, Dec 01 2024

nonn

Agrees with A378543 on odd n.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sums of divisors.

Cf. A000203, A353557, A378548.

Cf. also A378543, A378547.

A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A378549(n) = sumdiv(n,d,(1-A353557(d))*(n/d));

a(n) = Sum_{d|n} (1-A353557(d))*(n/d).

a(n) = A000203(n) - A378548(n).

cp's OEIS Frontend

A378546 a(n) is the sum of the divisors d of n for which A083345(n/d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

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A378543 Sum of divisors d of n such that n/d has an odd number of prime factors (counted with multiplicity).

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Author

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Crossrefs

Programs

PARI

Formula

A378549 Sum of divisors d of n such that n/d is not an odd number with an even number of prime factors (counted with multiplicity).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula