A344760 "Inverted variant" of A342002: a(n) = A342002(A289234(n)).

0, 1, 1, 5, 2, 7, 1, 7, 8, 31, 13, 41, 3, 11, 14, 43, 19, 53, 2, 9, 11, 37, 16, 47, 4, 13, 17, 49, 22, 59, 1, 9, 10, 41, 17, 55, 12, 59, 71, 247, 106, 317, 26, 87, 113, 331, 148, 401, 19, 73, 92, 289, 127, 359, 33, 101, 134, 373, 169, 443, 4, 15, 19, 59, 26, 73, 27, 89, 116, 337, 151, 407, 41, 117, 158, 421, 193, 491, 34

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..13860

Index entries for sequences related to primorial base

Formula

a(n) = A342001(A346101(n)) = A342002(A289234(n)).

Prog

(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]));
A342001(n) = (A003415(n) / A003557(n));
A346101(n) = { my(pr=1, p=2, m=1); while(n>0, my(d=n%p); if(d>0, m *= p^lift(1/Mod(d, p))); pr *= p; n \= p; p = nextprime(1+p)); return(m); };
A344760(n) = A342001(A346101(n));
(PARI)
A289234(n) = { my(pr=1, p=2, v=0); while(n>0, my (d=n%p); if(d>0, v += pr * lift(1/Mod(d, p))); pr *= p; n \= p; p = nextprime(1+p)); return(v); }; \\ From A289234.
A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A344760(n) = A342002(A289234(n));

Crossrefs

Cf. A003415, A003557, A276086, A342001, A342002, A289234, A346101.

Cf. also A344761, A344762.

Sequence in context: A263832 A351952 A342002 * A343422 A214969 A372925

Adjacent sequences: A344757 A344758 A344759 * A344761 A344762 A344763

Keyword

nonn,look

Author

Antti Karttunen, Jul 10 2021

Status

approved