A153011 Sum of proper divisors, minus the number of proper divisors, minus cototient of n, plus 1.

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 4, 0, 5, 0, 6, 0, 0, 0, 14, 0, 0, 2, 8, 0, 14, 0, 11, 0, 0, 0, 24, 0, 0, 0, 20, 0, 18, 0, 12, 8, 0, 0, 36, 0, 9, 0, 14, 0, 24, 0, 26, 0, 0, 0, 54, 0, 0, 10, 26, 0, 26, 0, 18, 0, 22, 0, 65, 0, 0, 10, 20, 0, 30, 0, 50, 10, 0, 0, 70, 0, 0, 0, 38, 0, 68, 0, 24, 0

Offset: 1

Author

Omar E. Pol, Dec 23 2008

Keywords

• easy
• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11880
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A000005, A000010, A000203, A001065, A032741, A051953, A152770.

Programs

Maple

A000203 := proc(n) numtheory[sigma](n) ; end: A000005 := proc(n) numtheory[tau](n) ; end: A152770 := proc(n) A000203(n)-A000005(n)-n+ 1; end: A051953 := proc(n) n - numtheory[phi](n) ; end: A153011 := proc(n) A152770(n)-A051953(n)+1 ; end: seq(A153011(n),n=1..120) ; # R. J. Mathar, Feb 19 2009

PARI

A153011(n) = (2+eulerphi(n)+sigma(n)-numdiv(n)-(2*n)); \\ Antti Karttunen, Oct 08 2018

Formula

a(n) = A152770(n) - A051953(n) + 1.

Extensions

More terms from R. J. Mathar, Feb 19 2009