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A364961
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Odd numbers k such that A005940(k) is either k itself or its descendant in Doudna-tree, A005940.
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3
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1, 3, 5, 25, 45, 49, 40131, 50575, 79625, 1486485, 1872507, 3403125
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OFFSET
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1,2
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COMMENTS
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Note that 1, 25, 45, 49 are so far the only known integers x for which A005940(x) = A003961(x).
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LINKS
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EXAMPLE
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Term (and its factorization) A005940(term) (and its factorization)
1 -> 1
3 -> 3
5 -> 5
25 = 5^2 -> 49 = 7^2
45 = 3^2 * 5 -> 175 = 5^2 * 7
49 = 7^2 -> 121 = 11^2
40131 = 3^2 * 7^3 * 13 -> 100847877 = 3 * 13^2 * 19^3 * 29
50575 = 5^2 * 7 * 17^2 -> 22467159 = 3^3 * 11^2 * 13 * 23^2
79625 = 5^3 * 7^2 * 13 -> 787365187 = 7 * 19^3 * 23^2 * 31
1486485 = 3^3 * 5 * 7 * 11^2 * 13 -> 25468143451205
= 5 * 7 * 13 * 17^3 * 19 * 23 * 29^2 * 31
1872507 = 3 * 7 * 13 * 19^3 -> 240245795625
= 3 * 5^4 * 11 * 17 * 23 * 31^3,
3403125 = 3^2 * 5^5 * 11^2 -> 2394659631669305
= 5 * 7^3 * 11 * 13^2 * 17^5 * 23^2.
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PROG
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(PARI)
Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
A156552(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]); res}; \\ From A156552
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
isA364961(n) = if(!(n%2), 0, my(k=A005940(n)); while(k>n, k = A252463(k)); (k==n));
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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