A294926 Number of proper divisors of n that are deficient (A005100).

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 4, 1, 3, 3, 4, 1, 4, 1, 5, 3, 3, 1, 5, 2, 3, 3, 5, 1, 6, 1, 5, 3, 3, 3, 5, 1, 3, 3, 6, 1, 6, 1, 5, 5, 3, 1, 6, 2, 5, 3, 5, 1, 5, 3, 6, 3, 3, 1, 7, 1, 3, 5, 6, 3, 6, 1, 5, 3, 7, 1, 6, 1, 3, 5, 5, 3, 6, 1, 7, 4, 3, 1, 7, 3, 3, 3, 7, 1, 8, 3, 5, 3, 3, 3, 7, 1, 5, 5, 7, 1, 6, 1, 7, 7

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = Sum_{d|n, d<n} A294934(d).

a(n) = A080226(n) - A294934(n).

a(n) + A294927(n) = A032741(n).

Mathematica

a[n_] := DivisorSum[n, 1 &, # < n && DivisorSigma[1, #] < 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)

Prog

(PARI) A294926(n) = sumdiv(n, d, (d<n)*(sigma(d)<(2*d))); \\ Antti Karttunen, Nov 14 2017

Crossrefs

Cf. A032741, A080226, A294886, A294927, A294928, A294929, A294934.

Sequence in context: A304795 A036459 A356159 * A079167 A304793 A199570

Adjacent sequences: A294923 A294924 A294925 * A294927 A294928 A294929

Keyword

nonn

Author

Antti Karttunen, Nov 14 2017

Status

approved