cp's OEIS Frontend

A369642 Composite numbers k, not squarefree semiprimes, such that k' is a sum of distinct primorial numbers, where k' stands for the arithmetic derivative of k, A003415.

%I A369642 #19 Feb 04 2024 09:03:29
%S A369642 9,16,28,30,45,108,112,136,189,198,210,212,225,236,244,246,282,290,
%T A369642 361,374,399,435,507,1480,1940,2132,2212,2308,2356,2524,2655,2766,
%U A369642 2802,3018,3054,3501,3590,3771,3938,4225,4454,4755,4809,5005,5763,6123,6771,9024,9936,10295,11881,12221,16296,22491,24389,26865
%N A369642 Composite numbers k, not squarefree semiprimes, such that k' is a sum of distinct primorial numbers, where k' stands for the arithmetic derivative of k, A003415.
%C A369642 Composite numbers k, not squarefree semiprimes, such that A327859(k) = A276086(A003415(k)) is squarefree number, or equally, k' is in A276156.
%C A369642 Squares that appear in this sequence: 9, 16, 225, 361, 4225, 11881, 1371241, 1635841, 225930961, 228644641, 229189321, 262083721, ...
%H A369642 Antti Karttunen, <a href="/A369642/b369642.txt">Table of n, a(n) for n = 1..2450</a>
%H A369642 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A369642 (PARI)
%o A369642 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369642 ismaxprimobasedigit_at_most(n,k) = { my(s=0, p=2); while(n, if((n%p)>k, return(0)); n = n\p; p = nextprime(1+p)); (1); };
%o A369642 A369640(n) = if(n<2 || isprime(n), 0, ismaxprimobasedigit_at_most(A003415(n),1));
%o A369642 isA369642(n) = (((bigomega(n)>2)||(bigomega(n)>omega(n))) && A369640(n));
%Y A369642 Sequence A369641 without any terms of A006881.
%Y A369642 Cf. A003415, A276086, A276156, A327859, A369647 (subsequence after its two initial terms).
%Y A369642 Nonsquarefree terms all occur in A369639.
%K A369642 nonn
%O A369642 1,1
%A A369642 _Antti Karttunen_, Jan 31 2024