A387710 -id:A387710 - cp's OEIS frontend

A387711 Numbers k for which A003959(k) > 2*k, where A003959 is multiplicative with a(p^e) = (p+1)^e.

4, 8, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 76, 78, 80, 81, 84, 88, 90, 92, 96, 100, 102, 104, 108, 112, 114, 116, 120, 124, 126, 128, 132, 135, 136, 138, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 174, 176, 180, 184, 186, 188, 189, 192, 196

Offset: 1

Antti Karttunen, Sep 06 2025

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A003959, A387710.
Disjoint union of A387712 and A387713. Positions of nonzero terms in A387715.
Subsequence of A005101, and of A246282.
After the initial 4 also a subsequence of A033942.

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
is_A387711(n) = (A003959(n)>(2*n));

A387720 Numbers k for which A107758(k) < 2*k, where A107758 is sigma+, multiplicative function with a(p^e) = 1+sigma(p^e).

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159

Offset: 1

Antti Karttunen, Sep 06 2025

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A107758.
Complement of (A052396 U A387721).
Cf. also A005100, A246281, A387710.

A107758(n) =  { my(f = factor(n)); prod(k=1, #f~, 1+sigma(f[k, 1]^f[k, 2])); };
is_A387720(n) = (A107758(n)<(2*n));

cp's OEIS Frontend

A387711 Numbers k for which A003959(k) > 2*k, where A003959 is multiplicative with a(p^e) = (p+1)^e.

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