A336645 -id:A336645 - cp's OEIS frontend

A326129 a(n) = gcd(A326127(n), A326128(n)).

1, 1, 2, 1, 4, 0, 6, 1, 1, 2, 10, 1, 12, 4, 6, 1, 16, 1, 18, 1, 10, 8, 22, 6, 1, 10, 2, 21, 28, 12, 30, 1, 18, 14, 22, 1, 36, 16, 22, 10, 40, 12, 42, 1, 4, 20, 46, 1, 1, 1, 30, 3, 52, 12, 38, 2, 34, 26, 58, 3, 60, 28, 2, 1, 46, 12, 66, 1, 42, 4, 70, 1, 72, 34, 2, 3, 58, 12, 78, 1, 1, 38, 82, 7, 62, 40, 54, 2, 88, 2, 70, 1, 58, 44, 70, 30

Offset: 1

Antti Karttunen, Jun 09 2019

nonn

Question: Are there any other numbers than those in A000396 that satisfy a(k) = A326128(k)?

See also comments in A336641, where all such k should reside. - Antti Karttunen, Jul 29 2020

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

Cf. A000396, A007913, A326126, A326127, A326128.

Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326060, A326062, A326130, A326140, A326144, A336641, A336645.

A326127(n) = (sigma(n)-core(n)-n);
A326128(n) = (n-core(n));
A326129(n) = gcd(A326127(n), A326128(n));

a(n) = n - A336645(n). - Antti Karttunen, Jul 29 2020

A336647 a(n) = n - A336566(n).

Original entry on oeis.org

0, 1, 1, 3, 1, 6, 1, 7, 8, 8, 1, 10, 1, 10, 9, 15, 1, 15, 1, 18, 11, 14, 1, 18, 24, 16, 25, 14, 1, 18, 1, 31, 15, 20, 13, 35, 1, 22, 17, 30, 1, 30, 1, 42, 42, 26, 1, 34, 48, 49, 21, 50, 1, 42, 17, 54, 23, 32, 1, 54, 1, 34, 62, 63, 19, 54, 1, 66, 27, 66, 1, 69, 1, 40, 74, 74, 19, 66, 1, 78, 80, 44, 1, 70, 23, 46, 33, 86

Offset: 1

Antti Karttunen, Jul 30 2020

sign

Some terms, for example a(600) and a(6552), are negative. - Georg Fischer, Jul 31 2020

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A000203, A007947, A057723, A308135, A336563, A336564, A336566.
Cf. A336555 (positions where differs from A336646).
Cf. A336565 (positions where a(n) = 2*n - A057723(n) = n - A336563(n)).
Cf. also A336645.

A007947(n) = factorback(factorint(n)[, 1]);
A057723(n) = { my(r=A007947(n)); (r*sigma(n/r)); };
A308135(n) = (sigma(n)-A057723(n));
A336563(n) = (A057723(n)-n);
A336564(n) = (n - A308135(n));
A336566(n) = gcd(A336563(n), A336564(n));
A336647(n) = (n - A336566(n));

a(n) = n - A336566(n).

A336646 a(n) = n - A326144(n).

Original entry on oeis.org

0, 1, 1, 3, 1, 6, 1, 7, 8, 8, 1, 10, 1, 10, 9, 15, 1, 15, 1, 18, 11, 14, 1, 18, 24, 16, 25, 14, 1, 18, 1, 31, 15, 20, 13, 35, 1, 22, 17, 30, 1, 30, 1, 42, 39, 26, 1, 34, 48, 49, 21, 50, 1, 42, 17, 54, 23, 32, 1, 54, 1, 34, 61, 63, 19, 54, 1, 66, 27, 66, 1, 69, 1, 40, 73, 74, 19, 66, 1, 78, 80, 44, 1, 70, 23, 46, 33, 86

Offset: 1

Antti Karttunen, Jul 30 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A007947, A066503, A326143, A326144.
Cf. A326145 (positions where coincides with A007947).
Cf. A336555 (positions where differs from A336647).
Cf. also A336645, A336647.

A007947(n) = factorback(factorint(n)[, 1]);
A066503(n) = (n - A007947(n));
A326143(n) = (sigma(n)-A007947(n)-n);
A326144(n) = gcd(A066503(n), A326143(n));
A336646(n) = (n - A326144(n));

cp's OEIS Frontend

A326129 a(n) = gcd(A326127(n), A326128(n)).

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Formula

A336647 a(n) = n - A336566(n).

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Formula

A336646 a(n) = n - A326144(n).

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