A334023 -id:A334023 - cp's OEIS frontend

A334024 Numbers k such that s(k) = s(k+1), where s(k) is the sum of unitary divisors of k that are larger than sqrt(k) (A334023).

24752, 101972, 14257705

Offset: 1

Amiram Eldar, Apr 12 2020

a(4) > 10^10.

			24752 is a term since A334023(24752) = A334023(24753) = 33896.

Cf. A064125, A324367, A334020, A334023.

s[n_] := DivisorSum[n, # &, #^2 > n && CoprimeQ[#, n/#] &]; Select[Range[1.5*10^7], s[#] == s[# + 1] &]

A334019 Sum of unitary divisors of n that are smaller than sqrt(n).

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 4, 1, 1, 3, 1, 5, 4, 3, 1, 4, 1, 3, 1, 5, 1, 11, 1, 1, 4, 3, 6, 5, 1, 3, 4, 6, 1, 12, 1, 5, 6, 3, 1, 4, 1, 3, 4, 5, 1, 3, 6, 8, 4, 3, 1, 13, 1, 3, 8, 1, 6, 12, 1, 5, 4, 15, 1, 9, 1, 3, 4, 5, 8, 12, 1, 6, 1, 3, 1, 15, 6

Offset: 1

Amiram Eldar, Apr 12 2020

nonn

			The unitary divisors of 12 are {1, 3, 4, 12}, 1 and 3 are smaller than sqrt(12) and their sum is 1 + 3 = 4, hence a(12) = 4.

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Cf. A034448, A070039, A077610, A334023.

a[n_] := DivisorSum[n, # &, #^2 < n && CoprimeQ[#, n/#] &]; Array[a, 100]

a(n) = sumdiv(n, d, if(gcd(d, n/d)==1 && dJinyuan Wang, Apr 12 2020

a(n) = A070039(n) for squarefree numbers (A005117) or squares of primes (A001248).

cp's OEIS Frontend

A334024 Numbers k such that s(k) = s(k+1), where s(k) is the sum of unitary divisors of k that are larger than sqrt(k) (A334023).

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