OFFSET
1,2
COMMENTS
Positions of records in A033273.
From Michael De Vlieger, Jan 04 2025: (Start)
Conjecture: This sequence includes all highly composite numbers (from A002182) except 2 and 6, but there are other terms in this sequence (e.g., a(3) = 8, a(9) = 72) that are not highly composite.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..571 (terms 1..146 from Ray Chandler)
Jorge Calero-Sanz and Luis Felipe Prieto-MartÃnez, Roots in the substitution group and in the group of Riordan matrices with ones in the main diagonal, Linear Algebra and its Applications 747, 234-253 (2026), see p. 247; arXiv preprint, arXiv:2509.25972 [math.GR], 2025. See p. 16.
Michael De Vlieger, Plot S(n) = P(omega(n))*m at (x,y) = (m, omega(n)), where S is the union of A002182 and this sequence, P is A002110, omega is A001221, and only select m that harbor S(n) shown. Shows the coincidence of many terms in this sequence with A002182. Blue represents m in A002182, gold m in both A002182 and this sequence; dark blue represents m in A002201 (and also in A002182), orange m in both A002201 and this sequence; red indicates terms in this sequence that are not in A002182. Green highlights terms in A002182 but are not determined to be in this sequence.
EXAMPLE
a(4)=12 because twelve has 4 nonprime divisors {1, 4, 6 and 12} whereas a(3)=8 has only 3; and twelve is the first number greater than eight which exhibits this property.
MATHEMATICA
l = 0; Do[ c = Count[PrimeQ[ Divisors[n] ], False]; If[c > l, l = c; Print[n] ], {n, 1, 10^6} ]
PROG
(PARI) lista(nn) = {my(m=0, nb); for (n=1, nn, nb = sumdiv(n, d, !isprime(d)); if (nb > m, m = nb; print1(n, ", ")); ); } \\ Michel Marcus, Jul 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 08 2001
EXTENSIONS
Alternate description and b-file from Ray Chandler, Aug 07 2010
STATUS
approved