A318877 Sum of divisors d of n for which 2*phi(d) < d.

0, 0, 0, 0, 0, 6, 0, 0, 0, 10, 0, 18, 0, 14, 0, 0, 0, 24, 0, 30, 0, 22, 0, 42, 0, 26, 0, 42, 0, 46, 0, 0, 0, 34, 0, 72, 0, 38, 0, 70, 0, 62, 0, 66, 0, 46, 0, 90, 0, 60, 0, 78, 0, 78, 0, 98, 0, 58, 0, 138, 0, 62, 0, 0, 0, 94, 0, 102, 0, 94, 0, 168, 0, 74, 0, 114, 0, 110, 0, 150, 0, 82, 0, 186, 0, 86, 0, 154, 0, 154, 0, 138, 0, 94, 0

Offset: 1

Author

Antti Karttunen, Sep 05 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A000203, A006519, A083254, A318875, A318876, A318879.

Cf. also A187795.

Programs

Mathematica

A318877[n_] := DivisorSum[n,  # &, 2*EulerPhi[#] < # &];
Array[A318877, 100] (* Paolo Xausa, Jul 08 2024 *)

PARI

A318877(n) = sumdiv(n,d,((2*eulerphi(d))
				

Formula

a(n) = Sum_{d|n} [2*phi(d) < d]*d, where [ ] are the Iverson brackets.

For all n >= 1, a(n) + A318876(n) + 2*(A006519(n)-1) = A000203(n).