A348930 a(n) = A038502(sigma(n)), where A038502 is fully multiplicative with a(3) = 1, and a(p) = p for any other prime p.

1, 1, 4, 7, 2, 4, 8, 5, 13, 2, 4, 28, 14, 8, 8, 31, 2, 13, 20, 14, 32, 4, 8, 20, 31, 14, 40, 56, 10, 8, 32, 7, 16, 2, 16, 91, 38, 20, 56, 10, 14, 32, 44, 28, 26, 8, 16, 124, 19, 31, 8, 98, 2, 40, 8, 40, 80, 10, 20, 56, 62, 32, 104, 127, 28, 16, 68, 14, 32, 16, 8, 65, 74, 38, 124, 140, 32, 56, 80, 62, 121, 14, 28

Offset

1,3

Comments

Note that a(A005820(4)) = A005820(4) and a(A005820(6)) = A005820(6), i.e., the fourth and sixth 3-perfect numbers, 459818240 and 51001180160 are among the fixed points of this sequence, precisely because they are also terms of A323653. As the former factorizes as 459818240 = 256 * 5 * 7 * 19 * 37 * 73, it must follow that a(256)/256 * a(5)/5 * a(7)/7 * a(19)/19 * a(37)/37 * a(73)/73 = 1, because ratio a(n)/n is multiplicative. See also comments in A348738.

Links

Table of n, a(n) for n=1..83.

Index entries for sequences related to sigma(n)

Formula

Multiplicative with a(p^e) = A038502(1 + p + p^2 + ... + p^e).

a(n) = A038502(A000203(n)).

For all n >= 1, A000265(a(n)) = A336457(n).

Mathematica

s[n_] := n / 3^IntegerExponent[n, 3]; Table[s[DivisorSigma[1, n]], {n, 1, 100}] (* Amiram Eldar, Nov 04 2021 *)

Prog

(PARI)
A038502(n) = (n/3^valuation(n, 3));
A348930(n) = A038502(sigma(n));

Crossrefs

Cf. A000203, A000265, A005820, A038502, A323653, A348738, A348931, A348932.

Cf. also A161942, A336457.

Sequence in context: A198506 A130882 A164106 * A159895 A113963 A071932

Adjacent sequences: A348927 A348928 A348929 * A348931 A348932 A348933

Keyword

nonn,mult

Author

Antti Karttunen, Nov 04 2021

Status

approved