A378521 Möbius transform of A048673.

1, 1, 2, 3, 3, 4, 5, 9, 10, 6, 6, 12, 8, 10, 12, 27, 9, 20, 11, 18, 20, 12, 14, 36, 21, 16, 50, 30, 15, 24, 18, 81, 24, 18, 30, 60, 20, 22, 32, 54, 21, 40, 23, 36, 60, 28, 26, 108, 55, 42, 36, 48, 29, 100, 36, 90, 44, 30, 30, 72, 33, 36, 100, 243, 48, 48, 35, 54, 56, 60, 36, 180, 39, 40, 84, 66, 60, 64, 41, 162, 250

Offset

1,3

Links

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

Index entries for sequences related to prime indices in the factorization of n

Formula

a(n) = Sum_{d|n} A008683(n/d)*A048673(d).

a(n) = A072451(A048673(n)).

a(n) = A055034(A003961(n)) = A349136(A003961(n)).

For n > 1, a(n) = A003972(n)/2 = A000010(A003961(n))/2.

Prog

(PARI)
A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A378521(n) = sumdiv(n, d, moebius(n/d)*A048673(d));
(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A378521(n) = if(1==n, n, eulerphi(A003961(n))/2);

Crossrefs

Cf. A000010, A003961, A003972, A008683, A048673, A055034, A072451, A349136.

Sequence in context: A157725 A372592 A238394 * A372595 A182503 A278288

Adjacent sequences: A378518 A378519 A378520 * A378522 A378523 A378524

Keyword

nonn,new

Author

Antti Karttunen, Nov 30 2024

Status

approved