A355595 Positions of records in A355593: Integers whose number of alternating divisors sets a new record.

1, 2, 4, 6, 12, 24, 36, 72, 144, 180, 360, 504, 630, 1080, 1260, 1890, 2520, 3780, 7560, 15120, 18900, 22680, 30240, 37800, 45360, 75600, 90720, 151200, 162540, 226800, 317520, 325080, 650160, 763560, 1137780, 1243620, 1527120, 2275560, 3054240, 3738420, 4551120, 6826680, 7476840, 14953680, 17445960, 21818160, 26168940, 36363600, 43636320, 52337880

Offset

1,2

Comments

Alternating integers are in A030141.

Corresponding records of number of alternating divisors are 1, 2, 3, 4, 6, 7, 9, 11, ...

Links

Table of n, a(n) for n=1..50.

Example

a(6) = 24 is in the sequence because A355593(24) = 7 is larger than any earlier value in A355593.

Mathematica

q[n_] := ! MemberQ[Differences[Mod[IntegerDigits[n], 2]], 0]; f[n_] := DivisorSum[n, 1 &, q[#] &]; fm = 0; s = {}; Do[fn = f[n]; If[fn > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 08 2022 *)

Crossrefs

Cf. A030141, A355593, A355594.

Similar, but with undulating divisors: A355304.

Sequence in context: A377140 A377708 A333665 * A050293 A330744 A330743

Adjacent sequences: A355592 A355593 A355594 * A355596 A355597 A355598

Keyword

nonn,base

Author

Bernard Schott, Jul 08 2022

Extensions

a(21)-a(36) from Amiram Eldar, Jul 08 2022

a(37)-a(50) from Charles R Greathouse IV, Jul 08 2022

Status

approved