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Indices of "late birds" in A090395 (denominator of d(n)/n): indices n such that A090395(k) > A090395(n) for all k > n.
2

%I #12 Apr 17 2022 09:26:58

%S 2,12,24,36,60,72,84,96,108,180,240,252,360,480,504,720,792,1260,1440,

%T 1680,1800,2160,2340,2640,3360,3600,5040,5280,6720,7920,10080,12600,

%U 15120,15840,18480,20160,21840,25200,30240,36960,40320,43680,55440,60480,65520

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

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

%C 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.

%C 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?

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

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

%Y 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).

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 15 2022