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

Author

Antti Karttunen, Nov 04 2021

Keywords

• nonn
• mult

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

• Index entries for sequences related to sigma(n)

Crossrefs

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

Cf. also A161942, A336457.

Programs

Mathematica

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

PARI

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