A065925 -id:A065925 - cp's OEIS frontend

A065926 Index values for new maxima in A065925.

1, 3, 5, 21, 25, 35, 55, 185, 265, 563, 569, 733, 3350, 3469, 6010, 6779, 10689, 11143, 14505, 18016, 30561, 31588, 37757, 59611, 65816, 67106, 75904, 118361, 214379, 241564, 255196, 414221, 648152, 703812, 881848, 1153107, 1277048, 1407769, 1719552, 1775846, 2722607, 3177728

Offset: 1

Jason Earls, Nov 28 2001

nonn

J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 99-100. ASIN: B002ACVZ6O [From Jason Earls, Nov 26 2009]

Cf. A065925, A065927.

sopf(n) = local(fac, i); fac=factor(n); sum(i=1,matsize(fac)[1],fac[i,1])
A065926(m)= {local(a,n,k); a=0; for(k=1,m,n=1; while(sopf(n)!=sopf(n+k), n++); if(n>a,a=n; print1(k,",")))} \\ Klaus Brockhaus

More terms from David Wasserman, Sep 19 2002

More terms from Sean A. Irvine, Sep 20 2023

A065927 Records in A065925.

Original entry on oeis.org

5, 7, 114, 209, 493, 516, 855, 1194, 1274, 2815, 2834, 3180, 3186, 5225, 6010, 8056, 8357, 8954, 11439, 13684, 14599, 15748, 17298, 17384, 17784, 20940, 25886, 36223, 36938, 41796, 53725, 64855, 67942, 69167, 72468, 79143, 79516, 86232, 96845, 120708, 125709

Offset: 1

Jason Earls, Nov 28 2001

nonn

Cf. A065925, A065926.

sopf(n) = local(fac, i); fac=factor(n); sum(i=1,matsize(fac)[1],fac[i,1])
A065927(m)= {local(a,n,k); a=0; for(k=1,m,n=1; while(sopf(n)!=sopf(n+k), n++); if(n>a,a=n; print1(n,",")))} // Klaus Brockhaus

More terms from David Wasserman, Sep 19 2002

More terms from Sean A. Irvine, Sep 21 2023

A065569 Smallest k such that omega(n+k) = omega(k).

Original entry on oeis.org

2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 4, 3, 2, 2, 3, 2, 5, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 14, 5, 4, 3, 2, 5, 4, 3, 2, 3, 2, 5, 4, 3, 2, 3, 2, 5, 4, 3, 2, 6, 8, 5, 4, 3, 2, 3, 2, 4, 3, 2, 4, 3, 2, 5, 4, 3, 2, 3, 2, 7, 8, 5, 4, 3, 2, 3, 2, 3, 2, 6, 10, 5, 4, 3, 2, 6, 6, 6, 15, 5, 4, 3, 2, 5, 4, 3, 2, 3, 2, 5, 4

Offset: 1

Jason Earls, Nov 30 2001

nonn

Harry J. Smith, Table of n, a(n) for n=1..1000

Cf. A001221, A065925.

a(n)= {for(k=1, oo, if(omega(k)==omega(n+k), return(k)))}

A280943 Least number k such that sopfr(k) = sopfr(k + n), where sopfr(k) is the integer log of k.

Original entry on oeis.org

5, 10, 7, 20, 7, 14, 20, 40, 13, 14, 21, 28, 14, 40, 19, 33, 11, 26, 56, 28, 49, 42, 115, 56, 35, 28, 31, 57, 11, 38, 50, 66, 63, 11, 17, 52, 11, 112, 42, 51, 22, 98, 11, 84, 57, 35, 52, 95, 138, 13, 33, 56, 22, 62, 77, 114, 61, 22, 39, 76, 44, 13, 91, 57, 70

Offset: 1

Paolo P. Lava, Jan 11 2017

			a(1) = 5 because 5 is the least number such that sopfr(5) = sopfr(5 + 1) = 5 .
a(2) = 10 because 10 is the least number such that sopfr(10) = sopfr(10 + 2) = 7 .

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A001414, A065925.

with(numtheory):P:=proc(q) local a,b,k,n; for n from 1 to q do for k from 1 to q do
a:=ifactors(k)[2]; b:=ifactors(k+n)[2];
if add(a[k][1]*a[k][2],k=1..nops(a))=add(b[k][1]*b[k][2],k=1..nops(b))
then print(k); break; fi; od; od; end: P(10^9);

cp's OEIS Frontend

A065926 Index values for new maxima in A065925.

Views

Author

Keywords

References

Crossrefs

Programs

PARI

Extensions

A065927 Records in A065925.

Views

Author

Keywords

Crossrefs

Programs

PARI

Extensions

A065569 Smallest k such that omega(n+k) = omega(k).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A280943 Least number k such that sopfr(k) = sopfr(k + n), where sopfr(k) is the integer log of k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple