A353011 Indices of "late birds" in A090395 (denominator of d(n)/n): indices n such that A090395(k) > A090395(n) for all k > n.

2, 12, 24, 36, 60, 72, 84, 96, 108, 180, 240, 252, 360, 480, 504, 720, 792, 1260, 1440, 1680, 1800, 2160, 2340, 2640, 3360, 3600, 5040, 5280, 6720, 7920, 10080, 12600, 15120, 15840, 18480, 20160, 21840, 25200, 30240, 36960, 40320, 43680, 55440, 60480, 65520

Offset

1,1

Comments

A090395(n) is the denominator of d(n)/n, where d = A000005 is the number of divisors.

The present sequence gives the indices of those terms of A090395 such that all subsequent terms are larger. This can be used to verify whether a number N is in A091896, which lists the numbers that don't occur in A090395.

It appears that a(n) is divisible by 12 for all n >= 2, by 5 for all n >= 18, by 24 (thus by 120) for all n > 23. Can somebody prove this?

Links

Table of n, a(n) for n=1..45.

Formula

a(n+1) > a(n).

Prog

(PARI) L=List(); forstep(n=m=65520, 1, -1, m>(m=min(A090395(n), m)) && listput(L, n)); Vecrev(L)

Crossrefs

Cf. A000005 (number of divisors), A090395 (denominator of A000005(n)/n), A091895 (index of first occurrence of n in A090395), A091896 (numbers that don't occur in A090395).

Sequence in context: A269841 A144551 A174457 * A110821 A262983 A356078

Adjacent sequences: A353008 A353009 A353010 * A353012 A353013 A353014

Keyword

nonn

Author

M. F. Hasler, Apr 15 2022

Status

approved