A344442 a(n) = A332844(n) - n.

0, 1, 1, 4, 1, 6, 1, 10, 5, 8, 1, 20, 1, 10, 9, 23, 1, 24, 1, 28, 11, 14, 1, 48, 7, 16, 17, 36, 1, 42, 1, 49, 15, 20, 13, 76, 1, 22, 17, 68, 1, 54, 1, 52, 39, 26, 1, 108, 9, 46, 21, 60, 1, 78, 17, 88, 23, 32, 1, 132, 1, 34, 49, 102, 19, 78, 1, 76, 27, 74, 1, 180, 1, 40, 53, 84, 19, 90, 1, 154, 54, 44, 1, 172, 23, 46

Offset: 1

Author

Antti Karttunen, May 23 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000010, A124315, A332844.

Programs

Mathematica

Table[DivisorSum[n, Boole[IntegerQ[(n/#)^(1/2)]] DivisorSigma[1, #] &] - n, {n, 86}] (* Michael De Vlieger, May 24 2021 *)

PARI

A332844(n) = sumdiv(n,d, issquare(n/d) * sigma(d));
A344442(n) = (A332844(n) - n);

Formula

a(n) = A332844(n) - n.

a(n) = Sum_{d|n} A000010(n/d) * (A124315(d)-1).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Pi^6/540 - 1 = 0.7803503... . - Amiram Eldar, Dec 04 2024