A332041 -id:A332041 - cp's OEIS frontend

A332039 Indices of records in A332038.

1, 12, 24, 60, 120, 240, 360, 720, 1440, 2880, 4320, 5760, 7200, 8640, 11520, 14400, 17280, 21600, 25920, 28800, 34560, 43200, 60480, 86400, 120960, 129600, 172800, 241920, 259200, 302400, 345600, 483840, 518400, 604800, 907200, 1036800, 1209600, 1814400, 2419200

Offset: 1

Amiram Eldar, Feb 05 2020

nonn

Numbers k such that isigma(x) = k has more solutions x than any smaller k, where isigma(x) is the sum of infinitary divisors of x (A049417).
The infinitary version of A145899.
The corresponding number of solutions for each term is 1, 2, 3, 5, 7, 12, 13, 20, ... (see the link for more values).

			There are 3 solutions to isigma(x) = 24: isigma(14) = isigma(15) = isigma(23) = 24. For all m < 24 there are 2 or fewer solutions to isigma(x) = m, thus 24 is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..53
Amiram Eldar, Table of n, a(n), A332038(a(n)) for n = 1..53

Cf. A145899, A049417, A289132, A332037, A332038, A332041.

fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 10000; v = Table[0, {m}]; Do[i = isigma[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

A332043 Indices of records in A332042.

Original entry on oeis.org

1, 6, 12, 24, 48, 72, 144, 288, 576, 864, 1152, 1440, 1728, 2160, 2304, 2880, 4320, 5760, 8640, 17280, 25920, 34560, 51840, 69120, 103680, 120960, 138240, 155520, 181440, 207360, 241920, 311040, 362880, 414720, 483840, 622080, 725760, 967680, 1244160, 1451520

Offset: 1

Amiram Eldar, Feb 05 2020

nonn

Numbers k such that psi(x) = k has more solutions x than any smaller k, where psi(x) is the Dedekind psi function (A001615).

The corresponding number of solutions for each term is 1, 2, 4, 5, 6, 9, 11, 17, ... (see the link for more values).

			There are 2 solutions to psi(x) = 6: psi(4) = psi(5) = 6. For all m < 6 there are no more than one solution to psi(x) = m, thus 6 is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..59
Amiram Eldar, Table of n, a(n), A332042(a(n)) for n = 1..59

Cf. A001615, A145899, A289132, A332037, A332039, A332041, A332042.

psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); m = 10000; v = Table[0, {m}]; Do[i = psi[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

cp's OEIS Frontend

A332039 Indices of records in A332038.

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