A318876 Sum of divisors d of n for which 2*phi(d) > d.

1, 1, 4, 1, 6, 4, 8, 1, 13, 6, 12, 4, 14, 8, 24, 1, 18, 13, 20, 6, 32, 12, 24, 4, 31, 14, 40, 8, 30, 24, 32, 1, 48, 18, 48, 13, 38, 20, 56, 6, 42, 32, 44, 12, 78, 24, 48, 4, 57, 31, 72, 14, 54, 40, 72, 8, 80, 30, 60, 24, 62, 32, 104, 1, 84, 48, 68, 18, 96, 48, 72, 13, 74, 38, 124, 20, 96, 56, 80, 6, 121, 42, 84, 32, 108, 44, 120, 12, 90, 78, 112, 24, 128, 48, 120, 4, 98, 57, 156, 31, 102, 72, 104, 14, 87

Offset: 1

Author

Antti Karttunen, Sep 05 2018

Keywords

• nonn

Comments

Not multiplicative as a(3) = 4, a(5) = 6 and a(7) = 8, but a(105) = 87, not a(3)*a(5)*a(7) = 4*6*8 = 192 = A000593(105).

Examples

			n = 105 has divisors [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, all others except the last one result a positive number, thus a(105) = 1+3+5+7+15+21+35 = 87.
		

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, A318874, A318877, A318878.

Cf. also A187793.

Differs from A000593 for the first time at n=105, where a(105) = 87, while A000593(105) = 192.

Programs

Mathematica

A318876[n_] := DivisorSum[n,  # &, 2*EulerPhi[#] > # &];
Array[A318876, 100] (* Paolo Xausa, Jul 08 2024 *)

PARI

A318876(n) = sumdiv(n,d,((2*eulerphi(d))>d)*d);

Formula

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

For all n >= 1, a(n) + A318877(n) + 2*(A006519(n)-1) = A000203(n).