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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).
4
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.
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
Indices of nonpositive terms in A374215.
Cf. A336702, A374219 (subsequences).
Sequence in context: A331773 A033286 A182724 * A342163 A098651 A087427
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 07 2024
STATUS
approved