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A349905 Arithmetic derivative of A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p). 8
0, 1, 1, 6, 1, 8, 1, 27, 10, 10, 1, 39, 1, 14, 12, 108, 1, 55, 1, 51, 16, 16, 1, 162, 14, 20, 75, 75, 1, 71, 1, 405, 18, 22, 18, 240, 1, 26, 22, 216, 1, 103, 1, 87, 95, 32, 1, 621, 22, 91, 24, 111, 1, 350, 20, 324, 28, 34, 1, 318, 1, 40, 135, 1458, 24, 119, 1, 123, 34, 131, 1, 945, 1, 44, 119, 147, 24, 151, 1, 837 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

FORMULA

a(n) = A003415(A003961(n)).

MATHEMATICA

f1[p_, e_] := e/p; d[1] = 0; d[n_] := n * Plus @@ f1 @@@ FactorInteger[n]; f2[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f2 @@@ FactorInteger[n]; a[n_] := d[s[n]]; Array[a, 100] (* Amiram Eldar, Dec 05 2021 *)

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A349905(n) = A003415(A003961(n));

CROSSREFS

Cf. A003415, A003961.

Cf. also A343221, A343222, A347964, A347965, A348937.

Sequence in context: A021622 A073228 A256853 * A258404 A244692 A248589

Adjacent sequences:  A349902 A349903 A349904 * A349906 A349907 A349908

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 05 2021

STATUS

approved

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Last modified August 7 12:01 EDT 2022. Contains 355985 sequences. (Running on oeis4.)