A278196 -id:A278196 - cp's OEIS frontend

A278197 Partition numbers (A000041) of the form 2^3 * k for odd k.

56, 792, 8118264, 92669720, 150198136, 1188908248, 1844349560, 3163127352, 4351078600, 5371315400, 7346629512, 11097645016, 16670689208, 18440293320, 684957390936, 6622987708040, 51820051838712, 77195892663512, 133978259344888, 197726516681672

Offset: 1

Colin Barker, Nov 15 2016

nonn

Also partition numbers having three times as many even divisors as odd divisors.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A275029, A278196, A278198, A278199, A278200, A278201.

Select[PartitionsP@ Range@ 250, Count[#, k_ /; EvenQ@ k] == 3 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)

maxk=300; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^3==0 & p\2^3%2==1, listput(L, p))); Vec(L)

A278198 Partition numbers (A000041) of the form 2^4 * k for odd k.

Original entry on oeis.org

176, 384276336, 2291320912, 5964539504, 10015581680, 290726957916112, 6486674127079088, 60105349839666544, 134819180623301520, 2332821198543892336, 14023788883518847344, 126891542690981418000, 320103136152993290544, 5852110108921301661040

Offset: 1

Colin Barker, Nov 15 2016

nonn

Also partition numbers having four times as many even divisors as odd divisors.

Colin Barker, Table of n, a(n) for n = 1..600

Cf. A275029, A278196, A278197, A278199, A278200, A278201.

Select[PartitionsP@ Range@ 518, Count[#, k_ /; EvenQ@ k] == 4 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)

maxk=600; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^4==0 & p\2^4%2==1, listput(L, p))); Vec(L)

A278199 Partition numbers (A000041) of the form 2^5 * k for odd k.

Original entry on oeis.org

4087968, 625846753120, 576672674947168, 1896564103591584, 21424521360255636320, 61382395164161775318496, 25744258930034131533263392, 54951205445179608281719072, 1317709210896221493178043552, 172557592110602218633091543840, 6647848746214407376439536432805536

Offset: 1

Colin Barker, Nov 15 2016

nonn

Also partition numbers having five times as many even divisors as odd divisors.

Colin Barker, Table of n, a(n) for n = 1..300

Cf. A275029, A278196, A278197, A278198, A278200, A278201.

Select[PartitionsP@ Range@ 1200, Count[#, k_ /; EvenQ@ k] == 5 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)

maxk=1400; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^5==0 & p\2^5%2==1, listput(L, p))); Vec(L)

A278200 Partition numbers (A000041) of the form 2^6 * k for odd k.

Original entry on oeis.org

2323520, 37027355200, 8030248384943040, 55733465144636286656, 134508188001572923840, 6179690078238084808000, 975509982873756796925504, 69523232218023552371152320, 638864582333908382360557376, 1151097146124113726578727360, 1204186073016375022219516992

Offset: 1

Colin Barker, Nov 15 2016

nonn

Also partition numbers having six times as many even divisors as odd divisors.

Colin Barker, Table of n, a(n) for n = 1..150

Cf. A275029, A278196, A278197, A278198, A278199, A278201.

Select[PartitionsP@ Range@ 1500, Count[#, k_ /; EvenQ@ k] == 6 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)

maxk=1000; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^6==0 & p\2^6%2==1, listput(L, p))); Vec(L)

A278201 Partition numbers (A000041) of the form 2^7 * k for odd k.

Original entry on oeis.org

541946240, 47826239745920, 49760750604354432757376, 18426207875324210441995136, 914345304752746677204951178080640, 377394877138559089794329589034333523822720, 33381228189530831120385246576357623531476650368, 23951815370456759593096244705083096637451017834880

Offset: 1

Colin Barker, Nov 15 2016

nonn

Also partition numbers having seven times as many even divisors as odd divisors.

Colin Barker, Table of n, a(n) for n = 1..100

Cf. A275029, A278196, A278197, A278198, A278199, A278200.

Select[PartitionsP@ Range@ 2000, Count[#, k_ /; EvenQ@ k] == 7 Count[#, k_ /; OddQ@ k] &@ Divisors@ # &] (* Michael De Vlieger, Nov 15 2016 *)

maxk=3000; L=List(); for(k=1, maxk, p=numbpart(k); if(p%2^7==0 & p\2^7%2==1, listput(L, p))); Vec(L)

A278779 Numbers m such that A000041(m) is of the form 2^2 * k for odd k.

Original entry on oeis.org

26, 30, 55, 58, 59, 62, 74, 78, 80, 84, 100, 108, 112, 113, 117, 124, 126, 135, 153, 187, 191, 200, 205, 258, 265, 280, 291, 310, 317, 323, 336, 337, 342, 344, 351, 352, 353, 358, 359, 365, 374, 380, 384, 404, 409, 416, 444, 445, 458, 481, 485, 492, 501, 503

Offset: 1

Colin Barker, Nov 28 2016

nonn

Numbers m such that A278478(m) = 2.

Also numbers m such that A000041(m) has twice as many even divisors as odd divisors.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A000041, A278196, A278780, A278781, A278782, A278783, A278784.

Positions of 2's in A278478.

Select[Range[3000], IntegerExponent[PartitionsP[#], 2] == 2 &] (* Amiram Eldar, May 25 2024 *)

isok(n) = valuation(numbpart(n), 2)==2;
select(n->isok(n), vector(1000, n, n))

A000041(a(n)) = A278196(n).

cp's OEIS Frontend

A278197 Partition numbers (A000041) of the form 2^3 * k for odd k.

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A278198 Partition numbers (A000041) of the form 2^4 * k for odd k.

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A278199 Partition numbers (A000041) of the form 2^5 * k for odd k.

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A278200 Partition numbers (A000041) of the form 2^6 * k for odd k.

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A278201 Partition numbers (A000041) of the form 2^7 * k for odd k.

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A278779 Numbers m such that A000041(m) is of the form 2^2 * k for odd k.

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