A171435 -id:A171435 - cp's OEIS frontend

A336699 a(n) = A000265(1+A000265(sigma(A000265(n)))), where A000265(k) gives the odd part of k, and sigma is the sum of divisors function.

1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 5, 7, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 7, 5, 3, 1, 1, 11, 1, 3, 1, 5, 1, 1, 1, 29, 1, 5, 1, 7, 3, 5, 1, 3, 1, 1, 1, 1, 1, 7, 1, 11, 1, 9, 5, 1, 1, 5, 7, 19, 5, 1, 3, 1, 1, 3, 1, 61, 11, 11, 1, 7, 3, 1, 1, 23, 5, 1, 1, 1, 1, 1, 1, 25, 29, 5, 1, 13, 5, 7, 1, 1

Offset: 1

Antti Karttunen, Aug 02 2020

See the "lacunae" in the scatter plot. - Antti Karttunen, Mar 27 2022

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Jon Maiga, Computer-generated formulas for A336699, Sequence Machine.
Index entries for sequences related to sigma(n)

Cf. A000203, A000265, A000593, A002131, A082903, A161942, A171435, A322250, A336698, A336700, A336701, A336844 [= a(A003961(n))], A351565.

A000265(n) = (n>>valuation(n,2));
A336699(n) = A000265(1+A000265(sigma(A000265(n))));

a(n) = A000265(1+A000265(A000593(n))) = A000265(1+A161942(A000265(n))).
a(n) = A336698(A000265(n)).
From Antti Karttunen, Mar 27 2022: (Start)
a(n) = A351565(A000593(n)).
[The following formulas were discovered by Sequence Machine]:
a(n) = A351565(A002131(n)) = A000265(1+A000265(A002131(n))).
a(n) = A336698(1+A322250(n)).
a(n) = A171435(A000593(n)+A082903(n)).
(End)

A171487 Product of odd prime anti-factors < n, with multiplicity.

Original entry on oeis.org

1, 1, 1, 9, 9, 1, 15, 15, 1, 21, 21, 25, 675, 27, 1, 33, 1155, 35, 39, 39, 1, 45, 45, 49, 2499, 51, 55, 3135, 57, 1, 63, 4095, 65, 69, 69, 1, 75, 5775, 77, 81, 81, 85, 7395, 87, 91, 8463, 8835, 95, 99, 99, 1, 105, 105, 1, 111, 111, 115, 13455, 13923, 14399, 14883, 15375

Offset: 1

Daniel Forgues, Dec 10 2009

nonn

Anti-factor is here defined as almost synonym with anti-divisor (except without the restriction of being less than n for anti-divisor.) ODD p^k is anti-factor (n) of n iff p^i, 1<=i<=k are anti-factors of n (note that this only applies to ODD anti-factors.)
In this sequence p < n, but p^k with k>=2 may be larger than n.
a(n) = 1 iff 2n-1 and 2n+1 are twin primes;
a(n) = 2n-1 iff 2n-1 is composite, 2n+1 is prime;
a(n) = 2n+1 iff 2n-1 is prime, 2n+1 is composite;
a(n) = (2n-1)(2n+1) iff 2n-1 and 2n+1 are both composite.

			3 is an anti-factor (and anti-divisor) of 5, and 3^2=9 is also an anti-factor (but not an anti-divisor since > 5) of 5.

Daniel Forgues, Table of n, a(n) for n=1..49999

Cf. A171435, A130799, A066272.

a(n) = {product of odd prime factors < 2n-1 of 2n-1, with multiplicity} * {product of odd prime factors < 2n+1 of 2n+1, with multiplicity}

GCD(a(n), a(n+1)) = {product of odd prime factors < 2n+1 of 2n+1, with multiplicity} (cf. A171435)

cp's OEIS Frontend

A336699 a(n) = A000265(1+A000265(sigma(A000265(n)))), where A000265(k) gives the odd part of k, and sigma is the sum of divisors function.

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