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

Author

Bernard Schott, Jul 08 2022

Keywords

• nonn
• base

Comments

Alternating integers are in A030141.

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

Examples

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

Crossrefs

Cf. A030141, A355593, A355594.

Similar, but with undulating divisors: A355304.

Programs

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 *)

Extensions

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

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