A326488 Numbers m such that A327566(m) = Sum_{k=1..m} isigma(k) is divisible by m, where isigma(k) is the sum of infinitary divisors of k (A049417).

1, 2, 160, 285, 2340, 2614, 8903, 81231, 171710, 182712, 434887, 2651907, 56517068, 143714354, 922484770, 5162883263, 39421525873

Offset

1,2

Comments

The infinitary version of A056550.

The corresponding quotients, A327566(a(n))/a(n), are 1, 2, 118, 209, 1711, 1910, 6506, 59357, 125473, 133513, 317781, 1937798, 41298052, 105014703, 674076450, 3772612983, 28806028088, ...

Links

Table of n, a(n) for n=1..17.

Example

2 is in the sequence since isigma(1) + isigma(2) = 1 + 3 = 4 is divisible by 2.

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); isigma[1] = 1; isigma[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) + 1); seq = {}; s = 0; Do[s = s + isigma [n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq

Crossrefs

Cf. A049417 (isigma), A327566 (sums of isigma).

Cf. A056550 (corresponding with sigma), A064611 (unitary), A307043 (exponential), A307161 (bi-unitary).

Sequence in context: A159030 A064071 A116638 * A170992 A179958 A272244

Adjacent sequences: A326485 A326486 A326487 * A326489 A326490 A326491

Keyword

nonn,more

Author

Amiram Eldar, Sep 20 2019

Status

approved