A294928 -id:A294928 - cp's OEIS frontend

A294927 Number of proper divisors of n that are nondeficient (A023196).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0

Offset: 1

Antti Karttunen, Nov 14 2017

nonn

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

Cf. A023196, A032741, A071395, A294887, A294926, A294928, A294929, A294936.

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

PARI
```
A294927(n) = sumdiv(n, d, (d=(2*d)));
```

a(n) = Sum_{d|n, dA294936(d).

a(n) + A294926(n) = A032741(n).

A294929 Number of proper divisors of n that are abundant (A005101).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6

Offset: 1

Antti Karttunen, Nov 14 2017

nonn

			The proper divisors of 24 are 1, 2, 3, 4, 6, 8, 12. Only one of these, 12, is abundant (in A005101), thus a(24) = 1.
The proper divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60. Six of these are abundant: 12, 20, 24, 30, 40, 60, thus a(120) = 6.

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

Cf. A005101, A032741, A080224, A294889, A294926, A294927, A294928, A294930, A294937.

Cf. also A294902.

a[n_] := Count[Most[Divisors[n]], ?(DivisorSigma[1, #] > 2*# &)]; Array[a, 100] (* _Amiram Eldar, Mar 14 2024 *)

PARI
```
A294929(n) = sumdiv(n, d, (d(2*d)));
```

a(n) = Sum_{d|n, dA294937(d).
a(n) = A080224(n) - A294937(n).
a(n) + A294928(n) = A032741(n).

A294888 Sum of nonabundant proper divisors of n.

Original entry on oeis.org

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 24, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 25, 1, 22, 17, 30, 1, 54, 1, 40, 33, 26, 1, 40, 8, 43, 21, 46, 1, 48, 17, 64, 23, 32, 1, 46, 1, 34, 41, 63, 19, 78, 1, 58, 27, 74, 1, 33, 1, 40, 49, 64, 19, 90, 1, 46, 40, 44, 1, 86, 23, 46, 33, 92, 1, 96, 21

Offset: 1

Antti Karttunen, Nov 14 2017

nonn

Sum of divisors of n smaller than n that are nonabundant numbers (in A263837).

			Proper divisors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45. Of these 1, 2, 3, 5, 6, 9, 10, 15 and 45 are in A263837, thus a(90) = 1+2+3+5+6+9+10+15+45 = 96.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sums of divisors

Cf. A001065, A263837, A294928, A294935, A294886, A294887, A294889.

Cf. A294900 (fixed points).

a[n_] := DivisorSum[n, Boole[# < n && DivisorSigma[1, #] <= 2#] * #&];
Array[a, 100] (* Jean-François Alcover, Nov 17 2017 *)

PARI
```
A294888(n) = sumdiv(n, d, (d
				
```

a(n) = Sum_{d|n, dA294935(d)*d.

a(n) + A294889(n) = A001065(n).

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

Original entry on oeis.org

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

Antti Karttunen, Nov 14 2017

nonn

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

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

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

A294926(n) = sumdiv(n, d, (dAntti Karttunen, Nov 14 2017

a(n) = Sum_{d|n, dA294934(d).
a(n) = A080226(n) - A294934(n).
a(n) + A294927(n) = A032741(n).

cp's OEIS Frontend

A294927 Number of proper divisors of n that are nondeficient (A023196).

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A294929 Number of proper divisors of n that are abundant (A005101).

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A294888 Sum of nonabundant proper divisors of n.

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

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