A354281 -id:A354281 - cp's OEIS frontend

A354282 Weird numbers k such that k+1 is the sum of a subset of the aliquot divisors of k.

70, 836, 4030, 5830, 7192, 7912, 10792, 17272, 45356, 83312, 91388, 113072, 222952, 243892, 254012, 388076, 410476, 786208, 1713592, 4145216, 4199030, 4632896, 6911512, 7257530, 7354304, 7607530, 9928792, 10402490, 10580624, 11339816, 11547352, 12052390, 13086016

Offset: 1

Amiram Eldar, May 22 2022

nonn

First differs from A258250 and A329190 at n=13.

There are 17270452 weird numbers below 10^10 and only 94 are in this sequence.

			70 is a term since it is a weird number, its aliquot divisors are {1, 2, 5, 7, 10, 14, 35} and 71 = 5 + 7 + 10 + 14 + 35.

Amiram Eldar, Table of n, a(n) for n = 1..94

Subsequence of A006037.
A354283 is a subsequence.
Cf. A005835, A258250, A329190, A354281.

q[n_] := Module[{d = Most @ Divisors[n], x, s, c}, If[Plus @@ d <= n, False, s = Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n + 1}]; c = SeriesCoefficient[s, #] & /@ (n + {0, 1}); c[[1]] == 0 && c[[2]] > 0]]; Select[Range[10000], q]

is(n, d=divisors(n)[^-1], s=vecsum(d))={s>n && !is_A005835(n, d, s) && is_A005835(n+1, d, s)}; \\ using is_A005835() by M. F. Hasler at A005835

A354283 Weird numbers k such that k-1 and k+1 are both sums of subsets of the aliquot divisors of k.

Original entry on oeis.org

70, 4030, 5830, 17272, 243892, 4199030, 11339816, 11547352, 13885970, 24450010, 31699430, 32284330, 34041370, 34169630, 42251930, 50761810, 67727110, 67820390, 85389368, 89283592, 141659096, 146764264, 162079768, 173482552, 259858324, 410832532, 411643576, 486224072

Offset: 1

Amiram Eldar, May 22 2022

nonn

There are 17270452 weird numbers below 10^10 and only 42 are in this sequence.

			70 is a term since it is a weird number, its aliquot divisors are {1, 2, 5, 7, 10, 14, 35}, 69 = 1 + 2 + 7 + 10 + 14 + 35, and 71 = 5 + 7 + 10 + 14 + 35.

Amiram Eldar, Table of n, a(n) for n = 1..42

Intersection of A354281 and A354282.
Subsequence of A006037.
Cf. A005835.

q[n_] := Module[{d = Most @ Divisors[n], x, s, c}, If[Plus @@ d <= n, False, s = Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n + 1}]; c = SeriesCoefficient[s, #] & /@ (n + {-1, 0, 1}); c[[1]] > 0 && c[[2]] == 0 && c[[3]] > 0]]; Select[Range[10000], q]

is(n, d=divisors(n)[^-1], s=vecsum(d))={s>n && !is_A005835(n, d, s) && is_A005835(n-1, d, s) && is_A005835(n+1, d, s)}; \\ using is_A005835() by M. F. Hasler at A005835

cp's OEIS Frontend

A354282 Weird numbers k such that k+1 is the sum of a subset of the aliquot divisors of k.

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