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A336548
Numbers k such that at least one pair sigma(p_i^e_i), sigma(p_j^e_j) [with i != j] share a prime factor, when k = p_1^e_1 * ... * p_h^e_h, where each p_i^e_i is the maximal power of prime p_i dividing k.
16
10, 15, 21, 22, 30, 33, 34, 35, 39, 40, 42, 46, 51, 52, 55, 57, 58, 60, 65, 66, 69, 70, 77, 78, 82, 84, 85, 87, 88, 90, 91, 93, 94, 95, 98, 102, 105, 106, 110, 111, 114, 115, 118, 119, 120, 123, 129, 130, 132, 133, 135, 136, 138, 140, 141, 142, 143, 145, 152, 154, 155, 156, 159, 160, 161, 164, 165, 166, 168, 170
OFFSET
1,1
COMMENTS
Numbers k for which A353802(k) = Product_{p^e||k} A051027(p^e) > A051027(k), i.e. numbers at which points A051027 is not multiplicative. The notation p^e||k means that p^e divides k, but p^(1+e) does not.
If x is present, then also multiples y*x are present for all y for which gcd(x,y) = 1.
Also numbers at which points A062401 and A353750 are not multiplicative. - Antti Karttunen, May 09 2022
LINKS
FORMULA
{k | A336562(k) > 0}. - Antti Karttunen, May 09 2022
EXAMPLE
10 = 2*5 is present as sigma(2) = 3 and sigma(5) = 6, and 3 and 6 share a prime factor (gcd(3,6) = 3). Also we see that sigma(sigma(2))*sigma(sigma(5)) = 4*12 = 48 > sigma(sigma(10)) = 39.
PROG
(PARI) isA336548(n) = !A336546(n);
CROSSREFS
Cf. A336357, A336558, A336560, A336561, A353807 (subsequences).
Positions of nonzero terms in A336562, in A353753 and in A353803.
Positions of terms larger than 1 in A353755, in A353784 and in A353806.
Subsequence of A024619.
Sequence in context: A045161 A105156 A108614 * A115708 A068992 A325901
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 25 2020
EXTENSIONS
The old definition moved to comments and replaced with a more generic, but equivalent definition by Antti Karttunen, May 09 2022
STATUS
approved