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Sum of proper divisors minus the number of proper divisors of pentagonal number A000326(n).
1

%I #11 Jul 02 2021 11:25:15

%S 0,0,11,11,10,18,67,71,60,32,187,351,30,46,519,337,128,220,577,483,

%T 366,286,507,1153,248,336,2489,847,70,818,871,2181,1108,116,2861,2275,

%U 694,130,2763,3645,100,2352,2823,1863,2278,158,3607,6617,636,920,6181,4019

%N Sum of proper divisors minus the number of proper divisors of pentagonal number A000326(n).

%H B. D. Swan, <a href="/A152986/b152986.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n)=A001065(A000326(n))-A032741(A000326(n)) = A152770(A000326(n)).

%p A000326 := proc(n) n*(3*n-1)/2 ; end: A000203 := proc(n) numtheory[sigma](n) ; end: A000005 := proc(n) numtheory[tau](n) ; end: A152770 := proc(n) A000203(n)-A000005(n)-n+1 ; end: A152986 := proc(n) A152770(A000326(n)) ; end: for n from 1 to 80 do printf("%a,",A152986(n)) ; od: # _R. J. Mathar_, Jan 03 2009

%t DivisorSigma[1,#]-#-DivisorSigma[0,#]+1&/@PolygonalNumber[5,Range[60]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 02 2021 *)

%Y Cf. A000005, A000203, A000326, A001065, A032741, A152770.

%K easy,nonn,look

%O 1,3

%A _Omar E. Pol_, Dec 22 2008

%E Extended by _R. J. Mathar_, Jan 03 2009