A262610 The values of sigma function (A000203) and the positive integers interleaved.

1, 1, 3, 2, 4, 3, 7, 4, 6, 5, 12, 6, 8, 7, 15, 8, 13, 9, 18, 10, 12, 11, 28, 12, 14, 13, 24, 14, 24, 15, 31, 16, 18, 17, 39, 18, 20, 19, 42, 20, 32, 21, 36, 22, 24, 23, 60, 24, 31, 25, 42, 26, 40, 27, 56, 28, 30, 29, 72, 30, 32, 31, 63, 32, 48, 33, 54, 34, 48, 35, 91, 36, 38, 37, 60, 38, 56, 39, 90, 40, 42, 41, 96, 42

Offset

1,3

Comments

a(n) is also the total area of the n-th symmetric set of regions in the two-dimensional diagram of the perspective view of the infinite stepped pyramid described in A245092 but according with the diagram as shown here in the Links section and assuming that the first square cell at the top of the structure has area = 1. Note that both the top view and the perspective view of the pyramid contain a hidden pattern which emerges from the front view of the pyramid. For more information see A237593, A262626.

Links

Table of n, a(n) for n=1..84.

Omar E. Pol, Illustration of initial terms (n = 1..32)

Maple

f:= n -> (numtheory:-sigma(n), n):
seq(f(n), n=1..100); # Robert Israel, Oct 22 2015

Mathematica

t = Range@ 42; Riffle[DivisorSigma[1, t], t] (* Michael De Vlieger, Oct 19 2015 *)

Prog

(PARI) vector(50, n, if (n % 2, sigma((n+1)/2), n/2)) \\ Michel Marcus, Oct 21 2015

Crossrefs

Cf. A000203, A245092, A236104, A237591, A237593, A237270, A237271, A262626.

Sequence in context: A147598 A023869 A024596 * A175508 A065375 A070961

Adjacent sequences: A262607 A262608 A262609 * A262611 A262612 A262613

Keyword

nonn,easy

Author

Omar E. Pol, Sep 26 2015

Extensions

a(12) corrected by Georg Fischer, Nov 02 2021

Status

approved