A367007 -id:A367007 - cp's OEIS frontend

A367008 Number of prime factors of n*2^n + 1, counted with multiplicity.

0, 1, 2, 2, 2, 2, 3, 3, 2, 2, 4, 2, 3, 3, 3, 3, 2, 4, 4, 4, 5, 2, 4, 4, 4, 4, 5, 4, 3, 3, 6, 6, 3, 2, 5, 2, 4, 3, 4, 3, 3, 4, 4, 5, 4, 4, 5, 5, 4, 5, 6, 3, 6, 3, 5, 4, 4, 5, 5, 4, 4, 7, 3, 3, 7, 5, 9, 5, 4, 5, 5, 6, 5, 5, 5, 5, 5, 4, 4, 6, 4, 4, 4, 5, 4, 7, 6

Offset: 0

Sean A. Irvine, Oct 31 2023

nonn

The numbers n*2^n+1 are called Cullen numbers.

Amiram Eldar, Table of n, a(n) for n = 0..865

Cf. A002064, A001222, A366899, A367007.

Table[PrimeOmega[n*2^n + 1], {n, 0, 100}] (* Amiram Eldar, Jan 06 2024 *)

a(n) = bigomega(n*2^n + 1); \\ Amiram Eldar, Jan 06 2024

a(n) = bigomega(n*2^n + 1) = A001222(A002064(n)).

A367009 Number of divisors of n*2^n + 1.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 8, 8, 4, 4, 12, 4, 8, 6, 8, 8, 4, 12, 16, 16, 16, 4, 16, 16, 16, 16, 24, 16, 6, 8, 48, 48, 8, 4, 32, 4, 12, 8, 12, 8, 8, 16, 16, 32, 16, 16, 32, 32, 16, 10, 64, 8, 64, 8, 32, 16, 12, 32, 32, 16, 16, 128, 8, 8, 96, 32, 256, 24, 16, 32, 32, 48

Offset: 0

Sean A. Irvine, Oct 31 2023

nonn

The numbers n*2^n+1 are called Cullen numbers.

Amiram Eldar, Table of n, a(n) for n = 0..865

Cf. A002064, A000005, A366898, A367007, A367008.

Table[DivisorSigma[0, n*2^n + 1], {n, 0, 100}] (* Amiram Eldar, Jan 06 2024 *)

a(n) = numdiv(n*2^n + 1); \\ Amiram Eldar, Jan 06 2024

a(n) = sigma0(n*2^n + 1) = A000005(A002064(n)).

A367010 a(n) is the sum of the divisors of n*2^n + 1.

Original entry on oeis.org

1, 4, 13, 31, 84, 192, 576, 1344, 2736, 5040, 13680, 24276, 56000, 153842, 308416, 538920, 1110276, 2909040, 5495040, 14446080, 31374720, 45955008, 106119552, 233997312, 527587200, 1184932800, 3247522560, 4365239040, 7784309910, 16265125632, 36250560000

Offset: 0

Sean A. Irvine, Oct 31 2023

nonn

The numbers n*2^n+1 are called Cullen numbers.

Amiram Eldar, Table of n, a(n) for n = 0..865

Cf. A002064, A000203, A063515, A367007, A367009.

DivisorSigma[1, Table[n*2^n+1, {n,0,30}]] (* Paul F. Marrero Romero, Dec 17 2023 *)

a(n) = sigma(n*2^n + 1) = A000203(A002064(n)).

cp's OEIS Frontend

A367008 Number of prime factors of n*2^n + 1, counted with multiplicity.

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A367009 Number of divisors of n*2^n + 1.

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A367010 a(n) is the sum of the divisors of n*2^n + 1.

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