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

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, 73, 19, 59, 41, 117, 193, 491, 158, 421, 34, 103, 172, 449, 137, 379, 27, 89, 151, 407, 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

Offset: 0

Author

Antti Karttunen, Apr 02 2022

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..20160
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A003415, A003557, A225901, A276076, A342001, A351952.

Cf. also A344760.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
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; };
A351952(n) = { my(u=A276076(n)); (A003415(u) / A003557(u)); };
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.
A351953(n) = A351952(A225901(n));

Formula

a(n) = A351952(A225901(n)) = A342001(A276076(A225901(n))).