cp's OEIS Frontend

A351953 a(n) = A351952(A225901(n)).

%I A351953 #8 Apr 03 2022 13:45:05
%S A351953 0,1,2,7,1,5,3,11,19,53,14,43,2,9,16,47,11,37,1,7,13,41,8,31,4,15,26,
%T A351953 73,19,59,41,117,193,491,158,421,34,103,172,449,137,379,27,89,151,407,
%U A351953 116,337,3,13,23,67,16,53,36,107,178,461,143,391,29,93,157,419,122,349,22,79,136,377,101,307,2,11,20,61
%N A351953 a(n) = A351952(A225901(n)).
%H A351953 Antti Karttunen, <a href="/A351953/b351953.txt">Table of n, a(n) for n = 0..20160</a>
%H A351953 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A351953 a(n) = A351952(A225901(n)) = A342001(A276076(A225901(n))).
%o A351953 (PARI)
%o A351953 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351953 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A351953 A276076(n) = { my(i=0,m=1,f=1,nextf); while((n>0),i=i+1; nextf = (i+1)*f; if((n%nextf),m*=(prime(i)^((n%nextf)/f));n-=(n%nextf));f=nextf); m; };
%o A351953 A351952(n) = { my(u=A276076(n)); (A003415(u) / A003557(u)); };
%o A351953 A225901(n) = { my(s=0, d, k=2); while(n, d=n%k; n=n\k; if(d, s=s+(k-d)*(k-1)!); k=k+1); return(s); }; \\ From A225901.
%o A351953 A351953(n) = A351952(A225901(n));
%Y A351953 Cf. A003415, A003557, A225901, A276076, A342001, A351952.
%Y A351953 Cf. also A344760.
%K A351953 nonn,base
%O A351953 0,3
%A A351953 _Antti Karttunen_, Apr 02 2022