A374218 After the initial 1, numbers k such that A347381 obtains its minimum value at k, of all the divisors d of k larger than one, where A347381 is the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree (A005940).

1, 2, 6, 15, 28, 77, 189, 496, 899, 945, 1271, 1403, 2125, 3127, 3139, 6375, 8128, 8383, 9261, 13843, 15247, 15631, 30240, 32760, 45151, 46305, 47263, 54053, 54653, 58339, 63767, 65473, 73813, 79567, 89951, 92783, 94957, 97969, 133907, 142859, 155011, 161257, 189209, 211621, 249001, 293323, 333961, 360883, 368063

Offset

1,2

Comments

Not all terms of A347383 are included here. The first missing ones are 226967, 925101, 961193, 4566661, 6031163, 6064439, 11234875.

Links

Antti Karttunen, Table of n, a(n) for n = 1..85

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Formula

{k | A347381(k) = A374204(k)}.

{k | A347381(k) <= A374214(k)}.

Example

189 has divisors 3, 7, 9, 21, 27, 63, 189 larger than 1. A347381 applied to them gives 1, 3, 2, 4, 3, 3, 1, so the largest divisor 189 gets minimal value 1 (which also occurs at the smallest prime divisor 3), thus 189 is included in this sequence.
496 has divisors 2, 4, 8, 16, 31, 62, 124, 248, 496 larger than 1. A347381 applied to them gives 0, 1, 2, 3, 10, 10, 9, 12, 0, so the largest divisor 496 gets minimal value 0 (which also occurs at the smallest prime divisor 2), thus 496 is included in this sequence.
1271 has divisors 31, 41, 1271 larger than 1. A347381 applied to them gives 10, 10, 9, of which minimal value 9 occurs at the largest divisor (1271 itself), thus 1271 is included in this sequence.

Prog

(PARI) isA374218(n) = if(n>2 && isprime(n), 0, my(w=A347381(n)); fordiv(n, d, if(d>1 && d<n && A347381(d)<w, return(0))); (1));

Crossrefs

Cf. A347381, A347383, A374204, A374214.

Indices of nonpositive terms in A374215.

Cf. A336702, A374219 (subsequences).

Sequence in context: A331773 A033286 A182724 * A342163 A098651 A087427

Adjacent sequences: A374215 A374216 A374217 * A374219 A374220 A374221

Keyword

nonn,new

Author

Antti Karttunen, Jul 07 2024

Status

approved