A387715 -id:A387715 - cp's OEIS frontend

A387713 Nonprimitive terms of A387711: numbers k for which A387715(k) > 1.

8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 90, 92, 96, 100, 104, 108, 112, 116, 120, 124, 126, 128, 132, 135, 136, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 198, 200, 204, 208, 210, 212, 216, 220, 224, 225, 228, 232, 234

Offset: 1

Antti Karttunen, Sep 06 2025

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

Cf. A003959.
Setwise difference A387711 \ A387712. Positions of terms > 1 in A387715.
Subsequence of A341610.

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A387715(n) = sumdiv(n,d,(A003959(d)>(2*d)));
is_A387713(n) = (A387715(n)>1);

{k | A387715(k) > 1}.

A387710 Numbers k for which A003959(k) < 2*k, where A003959 is multiplicative with a(p^e) = (p+1)^e.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 75, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98, 99, 101, 103, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 121, 122, 123, 125

Offset: 1

Antti Karttunen, Sep 06 2025

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

Cf. A003959, A387711.
Subsequence of A005100.
Subsequences: A000040, A001358\{4, 6}, A246281.
Positions of 0's in A387715.

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
is_A387710(n) = (A003959(n)<(2*n));

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

Original entry on oeis.org

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));

A387712 Primitive terms of A387711: numbers k for which A003959(k) > 2k, but for all whose proper divisors d|k, dA003959(d) <= 2d.

Original entry on oeis.org

4, 18, 27, 30, 42, 45, 50, 63, 66, 70, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 354, 366, 375, 402, 426, 438, 474, 498, 525, 534, 582, 606, 618, 625, 642, 654, 678, 686, 735, 762, 786, 822, 825, 834, 894, 906, 942, 975, 978, 1002, 1038, 1074, 1078, 1086, 1089, 1146, 1158, 1182, 1194, 1210, 1266, 1274, 1275

Offset: 1

Antti Karttunen, Sep 06 2025

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

Cf. A003959, A387711, A387713.
Positions of 1's in A387715.
Cf. also A091191, A337372.

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A387715(n) = sumdiv(n,d,(A003959(d)>(2*d)));
is_A387712(n) = (1==A387715(n));

{k | A387715(k) == 1}.

A387725 Number of unitary divisors d of n for which A107758(d) > 2*d, where A107758 is sigma+, multiplicative function with a(p^e) = 1+sigma(p^e).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 1, 0, 0, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 3

Offset: 1

Antti Karttunen, Sep 06 2025

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A107758, A387721 (positions of positive terms).

Cf. also A387715, A337345.

A107758(n) =  { my(f = factor(n)); prod(k=1, #f~, 1+sigma(f[k, 1]^f[k, 2])); };
A387725(n) = sumdiv(n,d,(1==gcd(d,n/d)) && (A107758(d)>(2*d)));

a(n) = Sum_{d|n} [gcd(d,n/d)==1 and A107758(d) > 2*d], where [ ] is the Iverson bracket.

cp's OEIS Frontend

A387713 Nonprimitive terms of A387711: numbers k for which A387715(k) > 1.

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A387710 Numbers k for which A003959(k) < 2*k, where A003959 is multiplicative with a(p^e) = (p+1)^e.

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

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A387712 Primitive terms of A387711: numbers k for which A003959(k) > 2*k, but for all whose proper divisors d|k, dA003959(d) <= 2*d.

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A387725 Number of unitary divisors d of n for which A107758(d) > 2*d, where A107758 is sigma+, multiplicative function with a(p^e) = 1+sigma(p^e).

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PARI

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A387712 Primitive terms of A387711: numbers k for which A003959(k) > 2k, but for all whose proper divisors d|k, dA003959(d) <= 2d.