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%I #8 Apr 03 2022 13:45:05
%S 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 73,19,59,41,117,193,491,158,421,34,103,172,449,137,379,27,89,151,407,
%U 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 a(n) = A351952(A225901(n)).
%H Antti Karttunen, <a href="/A351953/b351953.txt">Table of n, a(n) for n = 0..20160</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(n) = A351952(A225901(n)) = A342001(A276076(A225901(n))).
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A003557(n) = (n/factorback(factorint(n)[, 1]));
%o 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 A351952(n) = { my(u=A276076(n)); (A003415(u) / A003557(u)); };
%o 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(n) = A351952(A225901(n));
%Y Cf. A003415, A003557, A225901, A276076, A342001, A351952.
%Y Cf. also A344760.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Apr 02 2022