A344769 -id:A344769 - cp's OEIS frontend

A344765 a(n) = sigma(n) - A011772(n).

0, 0, 2, 0, 2, 9, 2, 0, 5, 14, 2, 20, 2, 17, 19, 0, 2, 31, 2, 27, 26, 25, 2, 45, 7, 30, 14, 49, 2, 57, 2, 0, 37, 38, 34, 83, 2, 41, 44, 75, 2, 76, 2, 52, 69, 49, 2, 92, 9, 69, 55, 59, 2, 93, 62, 72, 62, 62, 2, 153, 2, 65, 77, 0, 59, 133, 2, 110, 73, 124, 2, 132, 2, 78, 100, 84, 75, 156, 2, 122, 41, 86, 2, 176, 74, 89

Offset: 1

Antti Karttunen, May 30 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A001065, A011772, A294898, A344763, A344766, A344768 (Möbius transform), A344769.

A011772[n_] := Module[{m = 1}, While[Not[IntegerQ[m(m+1)/(2n)]], m++]; m];
a[n_] := DivisorSigma[1, n] - A011772[n];
Array[a, 100] (* Jean-François Alcover, Jun 12 2021 *)

PARI
```
A344765(n) = (sigma(n) - A011772(n));
```

a(n) = A000203(n) - A011772(n).
a(n) = A001065(n) + A344763(n).
a(n) = Sum_{d|n} A344768(d).
a(n) = A344769(n) - A294898(n).

A344763 a(n) = n - A011772(n).

Original entry on oeis.org

0, -1, 1, -3, 1, 3, 1, -7, 1, 6, 1, 4, 1, 7, 10, -15, 1, 10, 1, 5, 15, 11, 1, 9, 1, 14, 1, 21, 1, 15, 1, -31, 22, 18, 21, 28, 1, 19, 27, 25, 1, 22, 1, 12, 36, 23, 1, 16, 1, 26, 34, 13, 1, 27, 45, 8, 39, 30, 1, 45, 1, 31, 36, -63, 40, 55, 1, 52, 46, 50, 1, 9, 1, 38, 51, 20, 56, 66, 1, 16, 1, 42, 1, 36, 51, 43, 58, 56, 1, 55

Offset: 1

Antti Karttunen, May 30 2021

sign

Antti Karttunen, Table of n, a(n) for n = 1..16383
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A001065, A011772, A344764, A344765, A344769.

A011772[n_] := Module[{m = 1}, While[!IntegerQ[(m(m+1))/(2n)], m++]; m];
a[n_] := n - A011772[n];
Array[a, 100] (* Jean-François Alcover, Jun 12 2021 *)

PARI
```
A344763(n) = (n-A011772(n));
```

from sympy.ntheory.modular import crt
from sympy import factorint
from math import prod
from itertools import combinations
def A344763(n):
    plist = tuple(p**q for p, q in factorint(2*n).items())
    return 1-n if len(plist) == 1 else n-int(min(min(crt((m,2*n//m),(0,-1))[0],crt((2*n//m,m),(0,-1))[0]) for m in (prod(d) for l in range(1,len(plist)//2+1) for d in combinations(plist,l)))) # Chai Wah Wu, Jun 15 2022

a(n) = n - A011772(n).
a(n) = A344765(n) - A001065(n).
a(2^k) = 1-2^k. - Chai Wah Wu, Jun 15 2022

cp's OEIS Frontend

A344765 a(n) = sigma(n) - A011772(n).

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