%I #14 Jul 29 2023 14:36:02

%S 1,3,5,3125,7875,12005,13365,22869,23595,46475,703395,985439,2084775,

%T 2675673,13619125,19144125

%N Odd numbers k such that k is a multiple of A005941(k).

%C Odd numbers k such that k is a multiple of 1+A156552(k).

%C Sequence A005940(A364545(n)) sorted into ascending order.

%C This is a subsequence of A364561, so the comments given in A364564 apply also here (see also the example section).

%e In all these cases, the right hand side is a divisor of the left hand side:

%e Term (and its factorization) A005941(term)

%e 1 (unity) -> 1

%e 3 (prime) -> 3

%e 5 (prime) -> 5

%e 3125 = 5^5 -> 125 = 5^3

%e 7875 = 3^2 * 5^3 * 7 -> 375 = 3 * 5^3

%e 12005 = 5 * 7^4 -> 245 = 5 * 7^2

%e 13365 = 3^5 * 5 * 11 -> 1215 = 3^5 * 5

%e 22869 = 3^3 * 7 * 11^2 -> 847 = 7 * 11^2

%e 23595 = 3 * 5 * 11^2 * 13 -> 715 = 5 * 11 * 13

%e 46475 = 5^2 * 11 * 13^2 -> 845 = 5 * 13^2

%e 703395 = 3^2 * 5 * 7^2 * 11 * 29 -> 33495 = 3 * 5 * 7 * 11 * 29

%e 985439 = 7^3 * 13^2 * 17 -> 2873 = 13^2 * 17

%e 2084775 = 3 * 5^2 * 7 * 11 * 19^2 -> 12635 = 5 * 7 * 19^2

%e 2675673 = 3^5 * 7 * 11^2 * 13 -> 11583 = 3^4 * 11 * 13

%e 13619125 = 5^3 * 13 * 17^2 * 29 -> 36125 = 5^3 * 17^2

%e 19144125 = 3^2 * 5^3 * 7 * 11 * 13 * 17 -> 21879 = 3^2 * 11 * 13 * 17.

%o (PARI) A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After _David A. Corneth_'s program for A156552)

%o isA364551(n) = ((n%2)&&!(n%A005941(n)));

%Y Cf. A005940, A005941, A156552, A364545, A364549, A364564.

%Y Subsequence of A364561, which is a subsequence of A364560.

%K nonn,more

%O 1,2

%A _Antti Karttunen_, Jul 28 2023