A281006 a(n) = A000203(n) - A052928(n-1).

1, 3, 2, 5, 2, 8, 2, 9, 5, 10, 2, 18, 2, 12, 10, 17, 2, 23, 2, 24, 12, 16, 2, 38, 7, 18, 14, 30, 2, 44, 2, 33, 16, 22, 14, 57, 2, 24, 18, 52, 2, 56, 2, 42, 34, 28, 2, 78, 9, 45, 22, 48, 2, 68, 18, 66, 24, 34, 2, 110, 2, 36, 42, 65, 20, 80, 2, 60, 28, 76, 2, 125, 2, 42, 50, 66, 20, 92, 2, 108, 41, 46, 2, 142, 24, 48, 34, 94, 2

Offset: 1

Author

Omar E. Pol, Jan 23 2017

Keywords

• nonn

Comments

a(n) = 2 iff n is an odd prime (A065091).

Has a symmetric representation as a narrow pyramid with holes, in the same way as A249351.

Examples

			A000203    A052928     a(n)
.   1    -    0    =    1
.   3    -    0    =    3
.   4    -    2    =    2
.   7    -    2    =    5
.   6    -    4    =    2
.  12    -    4    =    8
...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A004526, A048050, A052928, A065091, A176059, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A245092, A249351, A262626, A279387, A281010.

Programs

PARI

A281006(n) = (sigma(n) - 2*((n-1)>>1)); \\ Antti Karttunen, Sep 25 2018

Formula

a(n) = sigma(n) - 2*floor((n - 1)/2) = A000203(n) - 2*A004526(n-1).

a(n) = A048050(n) + A176059(n), n >= 2.