OFFSET
2,1
COMMENTS
a(13) <= 31525197391593472. - David A. Corneth, Mar 20 2023
From Thomas Scheuerle, Mar 22 2023: (Start)
a(17) <= 15211807202738752817960438464512 and a(19) <= 2^190*11.
Conjecture: a(n) is of the form 2^b*p1^c*p2^d*...*pk^j with b > 0 and A020639(n) divides b*(c+1)*(d+1)*...*(j+1). (p1, p2, ..., pk are distinct odd prime numbers). (End)
FORMULA
a(2*m) = 4 for m >= 1.
a(6*m-3) = 64 for m >= 1.
From Thomas Scheuerle, Mar 22 2023: (Start)
Conjecture: For primes q > p, a(q) > a(p). If true, we could replace "<=" with "=" in the above formula. (End)
MATHEMATICA
a[n_] := Module[{k = 1, d}, While[Divisible[DivisorSigma[1, k], (d = DivisorSigma[0, k])] || !Divisible[DivisorSigma[n, k], d], k++]; k]; Array[a, 11, 2] (* Amiram Eldar, Mar 20 2023 *)
PROG
(PARI) isok(k, n) = my(f=factor(k), nd=numdiv(f)); (sigma(f) % nd) && !(sigma(f, n) % nd);
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Mar 20 2023
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Mohammed Yaseen, Mar 20 2023
STATUS
approved