A337196 -id:A337196 - cp's OEIS frontend

A337197 Position of the first occurrence of n in A337196, where A337196(x) is the 3-adic valuation of 1+A000265(sigma(x)).

1, 19, 67, 211, 643, 3667, 5827, 17491, 104971, 628123, 1795063, 2759719, 4251523, 12754579, 83086924

Offset: 0

Antti Karttunen and David A. Corneth, Aug 18 2020

a(16) = 393475036, but a(15) is larger than that, thus the sequence is nonmonotonic.

Cf. also A200849.

With[{s = Array[IntegerExponent[1 + #/2^IntegerExponent[#, 2], 3] &@ DivisorSigma[1, #] &, 10^6]}, Array[FirstPosition[s, #][[1]] &, Max[s] + 1, 0]] (* Michael De Vlieger, Feb 22 2021 *)

For all n >= 0, A337196(a(n)) = n, with no n occurring in A337196 before a(n).

A337194 a(n) = 1 + A000265(sigma(n)), where A000265 gives the odd part.

Original entry on oeis.org

2, 4, 2, 8, 4, 4, 2, 16, 14, 10, 4, 8, 8, 4, 4, 32, 10, 40, 6, 22, 2, 10, 4, 16, 32, 22, 6, 8, 16, 10, 2, 64, 4, 28, 4, 92, 20, 16, 8, 46, 22, 4, 12, 22, 40, 10, 4, 32, 58, 94, 10, 50, 28, 16, 10, 16, 6, 46, 16, 22, 32, 4, 14, 128, 22, 10, 18, 64, 4, 10, 10, 196, 38, 58, 32, 36, 4, 22, 6, 94, 122, 64, 22, 8, 28, 34

Offset: 1

Antti Karttunen, Aug 18 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

One more than A161942.

Cf. A000203, A000265, A336698, A337195, A337196.

A000265(n) = (n>>valuation(n,2));
A337194(n) = (1+A000265(sigma(n)));

a(n) = 1+A000265(A000203(n)).
a(n) = A336698(n) * 2^A337195(n).
A007949(a(n)) = A337196(n).

A337195 The 2-adic valuation of 1+A000265(sigma(n)), where A000265 gives the odd part.

Original entry on oeis.org

1, 2, 1, 3, 2, 2, 1, 4, 1, 1, 2, 3, 3, 2, 2, 5, 1, 3, 1, 1, 1, 1, 2, 4, 5, 1, 1, 3, 4, 1, 1, 6, 2, 2, 2, 2, 2, 4, 3, 1, 1, 2, 2, 1, 3, 1, 2, 5, 1, 1, 1, 1, 2, 4, 1, 4, 1, 1, 4, 1, 5, 2, 1, 7, 1, 1, 1, 6, 2, 1, 1, 2, 1, 1, 5, 2, 2, 1, 1, 1, 1, 6, 1, 3, 2, 1, 4, 1, 1, 1, 3, 1, 1, 1, 4, 6, 1, 2, 3, 1, 2, 2, 1, 1, 2

Offset: 1

Antti Karttunen, Aug 18 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A000265, A007814, A161942, A336698, A337194, A337196.

A007814(n) = valuation(n,2);
A000265(n) = (n>>A007814(n));
A337195(n) = A007814(1+A000265(sigma(n)));

a(n) = A007814(A337194(n)) = A007814(1+A000265(A000203(n))).

cp's OEIS Frontend

A337197 Position of the first occurrence of n in A337196, where A337196(x) is the 3-adic valuation of 1+A000265(sigma(x)).

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A337194 a(n) = 1 + A000265(sigma(n)), where A000265 gives the odd part.

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A337195 The 2-adic valuation of 1+A000265(sigma(n)), where A000265 gives the odd part.

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