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A107759 (+2)UnitarySigma(n): If n = Product p_i^r_i then (+2)UnitarySigma(n) = Product (2 + p_i^r_i), (+2)UnitarySigma(1) = 1. 2
1, 4, 5, 6, 7, 20, 9, 10, 11, 28, 13, 30, 15, 36, 35, 18, 19, 44, 21, 42, 45, 52, 25, 50, 27, 60, 29, 54, 31, 140, 33, 34, 65, 76, 63, 66, 39, 84, 75, 70, 43, 180, 45, 78, 77, 100, 49, 90, 51, 108, 95, 90, 55, 116, 91 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) = Sum_{d|n, gcd(d, n/d) = 1} usigma(d), where usigma = A034448. - Ilya Gutkovskiy, Mar 27 2020

EXAMPLE

(+2)UnitarySigma(12)=(2+3)*(2+4)=30.

MAPLE

A107759 := proc(n) local pf, p ; if n = 1 then 1; else pf := ifactors(n)[2] ; mul( 2+op(1, p)^op(2, p), p=pf) ; end if; end proc:

seq(A107759(n), n=1..60) ; # R. J. Mathar, Jan 07 2011

CROSSREFS

Cf. A007429, A034448, A054862, A107758.

Sequence in context: A154787 A233035 A250036 * A161627 A030667 A030677

Adjacent sequences:  A107756 A107757 A107758 * A107760 A107761 A107762

KEYWORD

nonn,mult,changed

AUTHOR

Yasutoshi Kohmoto, May 25 2005

STATUS

approved

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Last modified March 28 05:38 EDT 2020. Contains 333073 sequences. (Running on oeis4.)