A387729 Numbers k such that the powerful part of the sum of divisors of k (A387726) is greater than or equal to k, and sigma(k) is not itself a powerful number.

416, 780, 810, 1312, 1512, 2754, 3192, 4194, 4212, 5460, 6516, 6800, 8586, 12012, 12618, 13200, 14640, 18234, 18792, 21060, 21200, 24138, 24180, 24400, 27600, 28008, 28728, 31428, 31914, 32580, 33696, 35082, 38800, 40740, 43300, 46332, 46872, 47466, 52128, 54738, 56400, 57672, 58500, 58932, 68778, 72738, 74088

Offset

1,1

Comments

If a hypothetical odd perfect number is in A386428, then it must be reside also in this sequence.

Odd terms, given in A387719, are rare. The smallest one is a(10497) = 350561925.

Powerful terms (A001694) are: 74088, 121500, 222264, 1036800, 1871424, 1920996, 36360900, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..22000

Index entries for sequences related to sigma(n).

Prog

(PARI)
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); };
is_A387729(n) = { my(s=sigma(n)); (!ispowerful(s) && (A057521(s) >= n)); };

Crossrefs

Setwise difference A387727 \ A180097.

Cf. A000203, A001694, A057521, A386428, A387719 (odd terms), A387726.

Sequence in context: A172779 A056068 A224602 * A249006 A249471 A246897

Adjacent sequences: A387726 A387727 A387728 * A387730 A387731 A387732

Keyword

nonn

Author

Antti Karttunen, Sep 12 2025

Status

approved