A336641 -id:A336641 - 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

A336550 Numbers k such that A007947(k) divides sigma(k) and A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero.

Original entry on oeis.org

6, 24, 28, 96, 120, 234, 384, 496, 936, 1536, 1638, 6144, 8128, 24576, 42588, 98304, 393216, 1089270, 1572864, 6291456, 25165824, 33550336, 100663296, 115048440, 402653184, 1185125760, 1610612736

Offset: 1

Antti Karttunen, Jul 28 2020

Numbers k such that gcd(sigma(k)-A007947(k), A007947(k)) == A007947(k) are those in A175200. These are equal to k such that gcd(A326143(k), A007947(k)) = gcd(sigma(k)-A007947(k)-k, A007947(k)) are equal to A007947(k).
Sequence is infinite because all numbers of the form 6*4^n (A002023) are present.
Question: Are there any odd terms?

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Intersection of A175200 and A336552.
Cf. A007947, A326143, A336551.
Cf. A000396, A002023, A326145 (subsequences).
Cf. also A336641 for a similar construction.

A007947(n) = factorback(factorint(n)[, 1]);
isA336550(n) = { my(r=A007947(n), s=sigma(n), u=((n/r)-1)); (!(s%r) && (gcd(u,(s-r-n))==u)); };

A336642 One less than the largest square dividing n: a(n) = A008833(n)-1.

Original entry on oeis.org

0, 0, 0, 3, 0, 0, 0, 3, 8, 0, 0, 3, 0, 0, 0, 15, 0, 8, 0, 3, 0, 0, 0, 3, 24, 0, 8, 3, 0, 0, 0, 15, 0, 0, 0, 35, 0, 0, 0, 3, 0, 0, 0, 3, 8, 0, 0, 15, 48, 24, 0, 3, 0, 8, 0, 3, 0, 0, 0, 3, 0, 0, 8, 63, 0, 0, 0, 3, 0, 0, 0, 35, 0, 0, 24, 3, 0, 0, 0, 15, 80, 0, 0, 3, 0, 0, 0, 3, 0, 8, 0, 3, 0, 0, 0, 15, 0, 48, 8, 99, 0, 0, 0, 3, 0

Offset: 1

Antti Karttunen, Jul 28 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A008833.

Cf. also A336551, A336641, A336644.

PARI
```
A336642(n) = ((n/core(n))-1);
```

cp's OEIS Frontend

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

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A336550 Numbers k such that A007947(k) divides sigma(k) and A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero.

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Comments

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PARI

A336642 One less than the largest square dividing n: a(n) = A008833(n)-1.

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Author

Keywords

Links

Crossrefs

Programs

PARI