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

Author

M. F. Hasler, Apr 15 2022

Keywords

• nonn

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?

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).

Programs

PARI

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

Formula

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