A378736 Greatest divisor d of the n-th abundant number such that sigma(d) <= 2*d < A003961(d).

6, 9, 10, 8, 15, 9, 10, 21, 16, 27, 28, 15, 6, 35, 9, 39, 16, 28, 44, 45, 32, 50, 6, 52, 27, 28, 57, 15, 63, 44, 69, 35, 16, 75, 52, 32, 81, 28, 6, 44, 45, 6, 64, 98, 99, 50, 68, 52, 105, 27, 110, 6, 32, 76, 117, 16, 6, 63, 6, 130, 44, 135, 136, 92, 35, 6, 32, 147, 75, 152, 153, 154, 52, 6, 64, 81, 165, 28, 170, 171

Offset: 1

Author

Antti Karttunen, Dec 06 2024

Keywords

• nonn

Comments

There are no 1's in this sequence. See A378662, A378664 and A337372 for a proof.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A003961, A005101, A294935, A341612, A378664, A378735, A378737.

Cf. also A337372.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A294935(n) = (sigma(n)<=(2*n));
A341612(n) = ((sigma(n)<=(2*n))&&((2*n)<A003961(n)));
A378664(n) = { fordiv(n,d,if(A341612(n/d), return(n/d))); (1); };
k=0; n=0; while(k<20000, n++; if(!A294935(n), k++; print1(A378664(n),", ")));

Formula

a(n) = A378664(A005101(n)).

a(n) <= A378735(n).

Extensions

Unnecessary escape-clause removed from the definition by Antti Karttunen, Dec 12 2024