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A218767 Total number of divisors and anti-divisors of n. 2
1, 2, 3, 4, 4, 5, 5, 6, 5, 7, 5, 8, 6, 7, 7, 7, 7, 10, 5, 9, 7, 9, 7, 10, 8, 7, 9, 11, 5, 11, 7, 12, 9, 7, 9, 11, 7, 11, 9, 12, 6, 13, 7, 9, 13, 9, 7, 13, 9, 12, 7, 13, 9, 11, 9, 11, 9, 11, 9, 18, 6, 9, 13, 9, 9, 13, 11, 13, 7, 13, 7, 18, 9, 9, 11, 11, 13, 13, 5, 15, 11, 11, 9, 16, 12, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Or tau(n) + anti-tau(n), where anti-tau = A066272.

Total sum of divisors and anti-divisors of n or sigma(n) + A066417(n): 1, 3, 6, 10, 11, 16, 18, 23, 21, 32, 24, 41, 33, 40, 42, 45, 46, 67, 38, 66, 54, 72, 58, 83, 70, 66, 82, 102, 54, 108,...

Numbers n such that sigma(n) = n + anti-sigma(n): A074751.

Numbers n such that Chowla's function(n) = anti-sigma(n): 1, 2, 16, 60, 72,...

Number of divisors of n minus number of anti-divisors of n or tau(n) - anti-tau(n): 1, 2, 1, 2, 0, 3, -1, 2, 1, 1, -1, 4, -2, 1, 1, 3, -3, 2, -1, 3, 1, -1, -3, 6, -2, 1, -1, 1, -1, 5, -3, 0, -1, 1, -1, 7, -3, -3, -1, 4, -2, 3, -3, 3, -1,...

Product of number of divisors of n and number of anti-divisors of n, or tau(n)*anti-tau(n): 0, 0, 2, 3, 4, 4, 6, 8, 6, 12, 6, 12, 8, 12, 12, 10, 10, 24, 6, 18, 12, 20, 10, 16, 15, 12, 20, 30, 6, 24,...

Number of ways to write n as k*(k - m) with k divisor and m anti-divisor of n: 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,...

Numbers which are not of the form k*(k - m), k divisor, m anti-divisor (i.e., where the number of ways is zero): 1, 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 19, 21, 23, 24, 25, 26, 29,

LINKS

Table of n, a(n) for n=1..86.

FORMULA

a(n) = A000005(n) + A066272(n).

MAPLE

A218767 := proc(n)

numtheory[tau](n)+A066272(n) ;

end proc: # R. J. Mathar, Feb 16 2013

CROSSREFS

Cf. A000005, A000203, A001065, A066272, A066417, A027750, A048050, A130799.

Sequence in context: A200247 A056791 A333262 * A334863 A329202 A318994

Adjacent sequences: A218764 A218765 A218766 * A218768 A218769 A218770

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Feb 05 2013

STATUS

approved

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Last modified January 29 20:56 EST 2023. Contains 359926 sequences. (Running on oeis4.)