A334019 -id:A334019 - cp's OEIS frontend

A334020 Numbers k such that s(k) = s(k+1), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

2, 3, 4, 7, 8, 16, 31, 127, 186, 256, 318, 434, 473, 574, 582, 588, 730, 735, 819, 978, 1245, 1357, 1374, 1397, 1420, 1421, 1500, 1506, 1661, 1694, 1902, 1956, 1988, 2059, 2085, 2147, 2166, 2329, 2453, 2505, 2506, 2534, 2754, 2770, 2868, 2954, 2988, 3345, 3377

Offset: 1

Amiram Eldar, Apr 12 2020

nonn

			2 is a term since A334019(2) = A334019(3) = 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A064125, A324295, A334019,

s[n_] := DivisorSum[n, # &, #^2 < n && CoprimeQ[#, n/#] &]; Select[Range[3000], s[#] == s[# + 1] &]

A334021 Numbers k such that s(k) = s(k+1) = s(k+2), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

Original entry on oeis.org

2, 3, 7, 1420, 2505, 11860, 64060, 64485, 113413, 158020, 205365, 332658, 465272, 522764, 611085, 614538, 635053, 664033, 748484, 771138, 839213, 881565, 1011793, 1090788, 1190685, 1248645, 1306605, 1488088, 1607367, 1613190, 1836018, 1884914, 1911940, 2286913

Offset: 1

Amiram Eldar, Apr 12 2020

nonn

			2 is a term since A334019(2) = A334019(3) = A334019(4) = 1.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A324310, A334019, A334020.

s[n_] := DivisorSum[n, # &, #^2 < n && CoprimeQ[#, n/#] &]; seq={}; s1 = s[1]; s2 = s[2]; Do[s3 = s[n]; If[s1 == s2 && s2 == s3, AppendTo[seq, n - 2]]; s1 = s2; s2 = s3, {n, 3, 10^5}]; seq

A334022 Numbers k such that s(k) = s(k+1) = s(k+2) = s(k+3), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

Original entry on oeis.org

2, 46351754, 102841142, 158071592, 667930085, 851043553, 1097409992, 1580045430, 1595193655, 1698842487, 1919035496, 1951958341, 2279249234, 2507918727, 2520080695, 2741951910, 3335769314, 3654512455, 3713106152, 4209598844, 4351540982, 4369408604, 4480814965

Offset: 1

Amiram Eldar, Apr 12 2020

nonn

			2 is a term since A334019(2) = A334019(3) = A334019(4) = 1.

Cf. A325175, A334019, A334020, A334021.

s[n_] := DivisorSum[n, # &, #^2 < n && CoprimeQ[#, n/#] &]; seq={}; s1 = s[1]; s2 = s[2]; s3 = s[3]; Do[s4 = s[n]; If[s1 == s2 && s2 == s3 && s3 == s4, AppendTo[seq, n - 3]]; s1 = s2; s2 = s3; s3 = s4, {n, 4, 10^9}]; seq

A334023 Sum of unitary divisors of n that are larger than sqrt(n).

Original entry on oeis.org

0, 2, 3, 4, 5, 9, 7, 8, 9, 15, 11, 16, 13, 21, 20, 16, 17, 27, 19, 25, 28, 33, 23, 32, 25, 39, 27, 35, 29, 61, 31, 32, 44, 51, 42, 45, 37, 57, 52, 48, 41, 84, 43, 55, 54, 69, 47, 64, 49, 75, 68, 65, 53, 81, 66, 64, 76, 87, 59, 107, 61, 93, 72, 64, 78, 132, 67

Offset: 1

Amiram Eldar, Apr 12 2020

nonn

			The unitary divisors of 12 are {1, 3, 4, 12}, 4 and 12 are larger than sqrt(12) and their sum is 4 + 12 = 16, hence a(12) = 16.

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

Cf. A034448, A077610, A238535, A334019.

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

a(n) = sumdiv(n, d, if(gcd(d, n/d)==1 && d>sqrt(n), d)); \\ Jinyuan Wang, Apr 12 2020

a(n) = A238535(n) for squarefree numbers (A005117) or squares of primes (A001248).

cp's OEIS Frontend

A334020 Numbers k such that s(k) = s(k+1), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

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A334021 Numbers k such that s(k) = s(k+1) = s(k+2), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

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A334022 Numbers k such that s(k) = s(k+1) = s(k+2) = s(k+3), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

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A334023 Sum of unitary divisors of n that are larger than sqrt(n).

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